Unfinished Snakes and Ladders

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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An entry for Fortnightly Topic Challenge #40, have fun with non-Chess puzzle! ;)




Three young children: Red, Green, and Blue; were playing a classic game of Snakes and Ladders, when suddenly their mom called them to have a dinner.



When they came back to their room, they forgot whose turn it was even they were not sure either about the order of the play!



This was the last condition of the board, including the die. Could you tell them whose turn it is and the order of the play?



Unfinished Snakes and Ladders




Some notes:



  • They put their markers at tile 1 at the beginning.

  • They will win if their markers land on exactly at tile 100. They are using bouncing back version (roll 3 will move the marker from tile 99 to 98).

  • As long as they roll 6, they will get an additional extra roll after moving the marker.










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  • 1




    There are a couple of non-obvious things about this board. I'm guessing the straight ones are the ladders, and that a snake's head is always on a higher number than its tail. There are squares, however, that have one snake's tail, and another snake's head. How do these work? If you slide down the upper snake, will you immediately also slide down the lower one? There are also similarly interrupted ladders in there.
    – Bass
    6 hours ago










  • @Bass Ah right, I should clarify that the purple parallel-lines are ladders and the orange ones are snakes. The ladders should be used to go to higher number, but the snakes are used to go to lower number. For the interrupted ones, both are immediately used (e.g. landing on 39 will bring you to 25, same as landing on 20 will bring you to 25 too.)
    – athin
    5 hours ago










  • In the version of the game I used to play with my kids, if you land on a square where there is already a player, you sent him back to square 1. Does it apply here ?
    – Evargalo
    5 hours ago






  • 1




    @Evargalo No, it doesn't apply here
    – athin
    4 hours ago














up vote
7
down vote

favorite












An entry for Fortnightly Topic Challenge #40, have fun with non-Chess puzzle! ;)




Three young children: Red, Green, and Blue; were playing a classic game of Snakes and Ladders, when suddenly their mom called them to have a dinner.



When they came back to their room, they forgot whose turn it was even they were not sure either about the order of the play!



This was the last condition of the board, including the die. Could you tell them whose turn it is and the order of the play?



Unfinished Snakes and Ladders




Some notes:



  • They put their markers at tile 1 at the beginning.

  • They will win if their markers land on exactly at tile 100. They are using bouncing back version (roll 3 will move the marker from tile 99 to 98).

  • As long as they roll 6, they will get an additional extra roll after moving the marker.










share|improve this question

















  • 1




    There are a couple of non-obvious things about this board. I'm guessing the straight ones are the ladders, and that a snake's head is always on a higher number than its tail. There are squares, however, that have one snake's tail, and another snake's head. How do these work? If you slide down the upper snake, will you immediately also slide down the lower one? There are also similarly interrupted ladders in there.
    – Bass
    6 hours ago










  • @Bass Ah right, I should clarify that the purple parallel-lines are ladders and the orange ones are snakes. The ladders should be used to go to higher number, but the snakes are used to go to lower number. For the interrupted ones, both are immediately used (e.g. landing on 39 will bring you to 25, same as landing on 20 will bring you to 25 too.)
    – athin
    5 hours ago










  • In the version of the game I used to play with my kids, if you land on a square where there is already a player, you sent him back to square 1. Does it apply here ?
    – Evargalo
    5 hours ago






  • 1




    @Evargalo No, it doesn't apply here
    – athin
    4 hours ago












up vote
7
down vote

favorite









up vote
7
down vote

favorite











An entry for Fortnightly Topic Challenge #40, have fun with non-Chess puzzle! ;)




Three young children: Red, Green, and Blue; were playing a classic game of Snakes and Ladders, when suddenly their mom called them to have a dinner.



When they came back to their room, they forgot whose turn it was even they were not sure either about the order of the play!



This was the last condition of the board, including the die. Could you tell them whose turn it is and the order of the play?



Unfinished Snakes and Ladders




Some notes:



  • They put their markers at tile 1 at the beginning.

  • They will win if their markers land on exactly at tile 100. They are using bouncing back version (roll 3 will move the marker from tile 99 to 98).

  • As long as they roll 6, they will get an additional extra roll after moving the marker.










share|improve this question













An entry for Fortnightly Topic Challenge #40, have fun with non-Chess puzzle! ;)




Three young children: Red, Green, and Blue; were playing a classic game of Snakes and Ladders, when suddenly their mom called them to have a dinner.



When they came back to their room, they forgot whose turn it was even they were not sure either about the order of the play!



This was the last condition of the board, including the die. Could you tell them whose turn it is and the order of the play?



Unfinished Snakes and Ladders




Some notes:



  • They put their markers at tile 1 at the beginning.

  • They will win if their markers land on exactly at tile 100. They are using bouncing back version (roll 3 will move the marker from tile 99 to 98).

  • As long as they roll 6, they will get an additional extra roll after moving the marker.







board-games retrograde-analysis






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asked 9 hours ago









athin

6,35112358




6,35112358







  • 1




    There are a couple of non-obvious things about this board. I'm guessing the straight ones are the ladders, and that a snake's head is always on a higher number than its tail. There are squares, however, that have one snake's tail, and another snake's head. How do these work? If you slide down the upper snake, will you immediately also slide down the lower one? There are also similarly interrupted ladders in there.
    – Bass
    6 hours ago










  • @Bass Ah right, I should clarify that the purple parallel-lines are ladders and the orange ones are snakes. The ladders should be used to go to higher number, but the snakes are used to go to lower number. For the interrupted ones, both are immediately used (e.g. landing on 39 will bring you to 25, same as landing on 20 will bring you to 25 too.)
    – athin
    5 hours ago










  • In the version of the game I used to play with my kids, if you land on a square where there is already a player, you sent him back to square 1. Does it apply here ?
    – Evargalo
    5 hours ago






  • 1




    @Evargalo No, it doesn't apply here
    – athin
    4 hours ago












  • 1




    There are a couple of non-obvious things about this board. I'm guessing the straight ones are the ladders, and that a snake's head is always on a higher number than its tail. There are squares, however, that have one snake's tail, and another snake's head. How do these work? If you slide down the upper snake, will you immediately also slide down the lower one? There are also similarly interrupted ladders in there.
    – Bass
    6 hours ago










  • @Bass Ah right, I should clarify that the purple parallel-lines are ladders and the orange ones are snakes. The ladders should be used to go to higher number, but the snakes are used to go to lower number. For the interrupted ones, both are immediately used (e.g. landing on 39 will bring you to 25, same as landing on 20 will bring you to 25 too.)
    – athin
    5 hours ago










  • In the version of the game I used to play with my kids, if you land on a square where there is already a player, you sent him back to square 1. Does it apply here ?
    – Evargalo
    5 hours ago






  • 1




    @Evargalo No, it doesn't apply here
    – athin
    4 hours ago







1




1




There are a couple of non-obvious things about this board. I'm guessing the straight ones are the ladders, and that a snake's head is always on a higher number than its tail. There are squares, however, that have one snake's tail, and another snake's head. How do these work? If you slide down the upper snake, will you immediately also slide down the lower one? There are also similarly interrupted ladders in there.
– Bass
6 hours ago




There are a couple of non-obvious things about this board. I'm guessing the straight ones are the ladders, and that a snake's head is always on a higher number than its tail. There are squares, however, that have one snake's tail, and another snake's head. How do these work? If you slide down the upper snake, will you immediately also slide down the lower one? There are also similarly interrupted ladders in there.
– Bass
6 hours ago












@Bass Ah right, I should clarify that the purple parallel-lines are ladders and the orange ones are snakes. The ladders should be used to go to higher number, but the snakes are used to go to lower number. For the interrupted ones, both are immediately used (e.g. landing on 39 will bring you to 25, same as landing on 20 will bring you to 25 too.)
– athin
5 hours ago




@Bass Ah right, I should clarify that the purple parallel-lines are ladders and the orange ones are snakes. The ladders should be used to go to higher number, but the snakes are used to go to lower number. For the interrupted ones, both are immediately used (e.g. landing on 39 will bring you to 25, same as landing on 20 will bring you to 25 too.)
– athin
5 hours ago












In the version of the game I used to play with my kids, if you land on a square where there is already a player, you sent him back to square 1. Does it apply here ?
– Evargalo
5 hours ago




In the version of the game I used to play with my kids, if you land on a square where there is already a player, you sent him back to square 1. Does it apply here ?
– Evargalo
5 hours ago




1




1




@Evargalo No, it doesn't apply here
– athin
4 hours ago




@Evargalo No, it doesn't apply here
– athin
4 hours ago










3 Answers
3






active

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up vote
4
down vote













It is:




Green's Turn

The Turn order is: Red, Blue, Green




Reasoning:




Blue was the child who just rolled the 4, you know this because Green is only 3 spots from the beginning and if Red had rolled a 4 he would've started the last turn from an impossible position on top a chute

Because of Green's position he must have only taken 1 or 2 moves from the beginning of the game. Both Red and Blue's position is impossible to reach in 1 turn, as even with the roll again on 6 rule, they get trapped in an infinite loop with the slide from 31 to 7.

There are 9 effectively different starting positions for turn 2, a unique one for if their last roll landed them on one of the escape ladders or their last die roll. It is impossible to reach Red's current position or Blue's known starting position from any of these 9 starting positions, meaning that Red has already taken 3 turns, Blue has just taken his 3rd turn and Green must go next.







share|improve this answer










New contributor




Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.













  • 2




    couldn't red have been on 95 the previous turn (atop a ladder)
    – Destructible Lemon
    7 hours ago










  • He couldn't have gotten to 95 in 1 turn though, so that might have been his starting spot from the last turn but it was on the third turn.
    – Evan Capstick
    6 hours ago


















up vote
1
down vote













Assuming the order of players to roll the dice is R B G,

the next player after they come back from dinner will be




Green




Because




On the first round:

R rolled 6-6-6-6-5 => ends in 30.

B rolled 6-6-6-6-5 => ends in 30.

G rolled 1 => ends in 2.

On the second round:

R rolled 6-6-5 => ends in 66.

B rolled 6-6-3 => ends in 77.

G rolled 2 => ends in 4.

On the third round:

R rolled 6-6-6-6-6-3 => ends in 99.

B rolled 6-6-4 => ends in 77 again.

Last roll was 4 and now it is G's turn.







share|improve this answer



























    up vote
    1
    down vote













    The other guys already got the answer (with possibly slightly dubious arguments), but the explanations are a bit hard to follow without pictures, so here's one:




    enter image description here




    Legend:



    • Red square: after turn 1, you are in one of these.

    • Green square: after turn 2, you are in one of these, or in some red square.

    • Red circle with R: if Red was the last player to move, Red's turn started at one of these.

    From there, the solution is pretty simple:




    1. Green has had either one or two turns.

    2. Therefore, Red has had at most three turns.

    3. Therefore, because no green square overlaps with a letter R, Red was not the last to move.

    3.1 There is no way to get to Red's current position with 2 turns only, So Red has taken at least 3 turns. Combined with point 2, Red has taken exactly 3 turns.

    4. Therefore, Green has taken 2 turns, rolling first 1, then 2.




    So the only remaining things to check are that




    5. Red really can get to its current square in 3 turns (yes, starting the third turn at 66, 62, 60 or 56.)

    6. Blue can get to its current spot in 3 moves, ending with a 4 (yes, starting the third turn at 58, 60, 65, or indeed 77)




    So finally, the answer is




    It's Green's turn, and after that it's time for the fourth round, with Red playing next.







    share|improve this answer






















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      3 Answers
      3






      active

      oldest

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      3 Answers
      3






      active

      oldest

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      active

      oldest

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      active

      oldest

      votes








      up vote
      4
      down vote













      It is:




      Green's Turn

      The Turn order is: Red, Blue, Green




      Reasoning:




      Blue was the child who just rolled the 4, you know this because Green is only 3 spots from the beginning and if Red had rolled a 4 he would've started the last turn from an impossible position on top a chute

      Because of Green's position he must have only taken 1 or 2 moves from the beginning of the game. Both Red and Blue's position is impossible to reach in 1 turn, as even with the roll again on 6 rule, they get trapped in an infinite loop with the slide from 31 to 7.

      There are 9 effectively different starting positions for turn 2, a unique one for if their last roll landed them on one of the escape ladders or their last die roll. It is impossible to reach Red's current position or Blue's known starting position from any of these 9 starting positions, meaning that Red has already taken 3 turns, Blue has just taken his 3rd turn and Green must go next.







      share|improve this answer










      New contributor




      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.













      • 2




        couldn't red have been on 95 the previous turn (atop a ladder)
        – Destructible Lemon
        7 hours ago










      • He couldn't have gotten to 95 in 1 turn though, so that might have been his starting spot from the last turn but it was on the third turn.
        – Evan Capstick
        6 hours ago















      up vote
      4
      down vote













      It is:




      Green's Turn

      The Turn order is: Red, Blue, Green




      Reasoning:




      Blue was the child who just rolled the 4, you know this because Green is only 3 spots from the beginning and if Red had rolled a 4 he would've started the last turn from an impossible position on top a chute

      Because of Green's position he must have only taken 1 or 2 moves from the beginning of the game. Both Red and Blue's position is impossible to reach in 1 turn, as even with the roll again on 6 rule, they get trapped in an infinite loop with the slide from 31 to 7.

      There are 9 effectively different starting positions for turn 2, a unique one for if their last roll landed them on one of the escape ladders or their last die roll. It is impossible to reach Red's current position or Blue's known starting position from any of these 9 starting positions, meaning that Red has already taken 3 turns, Blue has just taken his 3rd turn and Green must go next.







      share|improve this answer










      New contributor




      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.













      • 2




        couldn't red have been on 95 the previous turn (atop a ladder)
        – Destructible Lemon
        7 hours ago










      • He couldn't have gotten to 95 in 1 turn though, so that might have been his starting spot from the last turn but it was on the third turn.
        – Evan Capstick
        6 hours ago













      up vote
      4
      down vote










      up vote
      4
      down vote









      It is:




      Green's Turn

      The Turn order is: Red, Blue, Green




      Reasoning:




      Blue was the child who just rolled the 4, you know this because Green is only 3 spots from the beginning and if Red had rolled a 4 he would've started the last turn from an impossible position on top a chute

      Because of Green's position he must have only taken 1 or 2 moves from the beginning of the game. Both Red and Blue's position is impossible to reach in 1 turn, as even with the roll again on 6 rule, they get trapped in an infinite loop with the slide from 31 to 7.

      There are 9 effectively different starting positions for turn 2, a unique one for if their last roll landed them on one of the escape ladders or their last die roll. It is impossible to reach Red's current position or Blue's known starting position from any of these 9 starting positions, meaning that Red has already taken 3 turns, Blue has just taken his 3rd turn and Green must go next.







      share|improve this answer










      New contributor




      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      It is:




      Green's Turn

      The Turn order is: Red, Blue, Green




      Reasoning:




      Blue was the child who just rolled the 4, you know this because Green is only 3 spots from the beginning and if Red had rolled a 4 he would've started the last turn from an impossible position on top a chute

      Because of Green's position he must have only taken 1 or 2 moves from the beginning of the game. Both Red and Blue's position is impossible to reach in 1 turn, as even with the roll again on 6 rule, they get trapped in an infinite loop with the slide from 31 to 7.

      There are 9 effectively different starting positions for turn 2, a unique one for if their last roll landed them on one of the escape ladders or their last die roll. It is impossible to reach Red's current position or Blue's known starting position from any of these 9 starting positions, meaning that Red has already taken 3 turns, Blue has just taken his 3rd turn and Green must go next.








      share|improve this answer










      New contributor




      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this answer



      share|improve this answer








      edited 7 hours ago





















      New contributor




      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      answered 8 hours ago









      Evan Capstick

      613




      613




      New contributor




      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Evan Capstick is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      • 2




        couldn't red have been on 95 the previous turn (atop a ladder)
        – Destructible Lemon
        7 hours ago










      • He couldn't have gotten to 95 in 1 turn though, so that might have been his starting spot from the last turn but it was on the third turn.
        – Evan Capstick
        6 hours ago













      • 2




        couldn't red have been on 95 the previous turn (atop a ladder)
        – Destructible Lemon
        7 hours ago










      • He couldn't have gotten to 95 in 1 turn though, so that might have been his starting spot from the last turn but it was on the third turn.
        – Evan Capstick
        6 hours ago








      2




      2




      couldn't red have been on 95 the previous turn (atop a ladder)
      – Destructible Lemon
      7 hours ago




      couldn't red have been on 95 the previous turn (atop a ladder)
      – Destructible Lemon
      7 hours ago












      He couldn't have gotten to 95 in 1 turn though, so that might have been his starting spot from the last turn but it was on the third turn.
      – Evan Capstick
      6 hours ago





      He couldn't have gotten to 95 in 1 turn though, so that might have been his starting spot from the last turn but it was on the third turn.
      – Evan Capstick
      6 hours ago











      up vote
      1
      down vote













      Assuming the order of players to roll the dice is R B G,

      the next player after they come back from dinner will be




      Green




      Because




      On the first round:

      R rolled 6-6-6-6-5 => ends in 30.

      B rolled 6-6-6-6-5 => ends in 30.

      G rolled 1 => ends in 2.

      On the second round:

      R rolled 6-6-5 => ends in 66.

      B rolled 6-6-3 => ends in 77.

      G rolled 2 => ends in 4.

      On the third round:

      R rolled 6-6-6-6-6-3 => ends in 99.

      B rolled 6-6-4 => ends in 77 again.

      Last roll was 4 and now it is G's turn.







      share|improve this answer
























        up vote
        1
        down vote













        Assuming the order of players to roll the dice is R B G,

        the next player after they come back from dinner will be




        Green




        Because




        On the first round:

        R rolled 6-6-6-6-5 => ends in 30.

        B rolled 6-6-6-6-5 => ends in 30.

        G rolled 1 => ends in 2.

        On the second round:

        R rolled 6-6-5 => ends in 66.

        B rolled 6-6-3 => ends in 77.

        G rolled 2 => ends in 4.

        On the third round:

        R rolled 6-6-6-6-6-3 => ends in 99.

        B rolled 6-6-4 => ends in 77 again.

        Last roll was 4 and now it is G's turn.







        share|improve this answer






















          up vote
          1
          down vote










          up vote
          1
          down vote









          Assuming the order of players to roll the dice is R B G,

          the next player after they come back from dinner will be




          Green




          Because




          On the first round:

          R rolled 6-6-6-6-5 => ends in 30.

          B rolled 6-6-6-6-5 => ends in 30.

          G rolled 1 => ends in 2.

          On the second round:

          R rolled 6-6-5 => ends in 66.

          B rolled 6-6-3 => ends in 77.

          G rolled 2 => ends in 4.

          On the third round:

          R rolled 6-6-6-6-6-3 => ends in 99.

          B rolled 6-6-4 => ends in 77 again.

          Last roll was 4 and now it is G's turn.







          share|improve this answer












          Assuming the order of players to roll the dice is R B G,

          the next player after they come back from dinner will be




          Green




          Because




          On the first round:

          R rolled 6-6-6-6-5 => ends in 30.

          B rolled 6-6-6-6-5 => ends in 30.

          G rolled 1 => ends in 2.

          On the second round:

          R rolled 6-6-5 => ends in 66.

          B rolled 6-6-3 => ends in 77.

          G rolled 2 => ends in 4.

          On the third round:

          R rolled 6-6-6-6-6-3 => ends in 99.

          B rolled 6-6-4 => ends in 77 again.

          Last roll was 4 and now it is G's turn.








          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 3 hours ago









          ImongMama

          1415




          1415




















              up vote
              1
              down vote













              The other guys already got the answer (with possibly slightly dubious arguments), but the explanations are a bit hard to follow without pictures, so here's one:




              enter image description here




              Legend:



              • Red square: after turn 1, you are in one of these.

              • Green square: after turn 2, you are in one of these, or in some red square.

              • Red circle with R: if Red was the last player to move, Red's turn started at one of these.

              From there, the solution is pretty simple:




              1. Green has had either one or two turns.

              2. Therefore, Red has had at most three turns.

              3. Therefore, because no green square overlaps with a letter R, Red was not the last to move.

              3.1 There is no way to get to Red's current position with 2 turns only, So Red has taken at least 3 turns. Combined with point 2, Red has taken exactly 3 turns.

              4. Therefore, Green has taken 2 turns, rolling first 1, then 2.




              So the only remaining things to check are that




              5. Red really can get to its current square in 3 turns (yes, starting the third turn at 66, 62, 60 or 56.)

              6. Blue can get to its current spot in 3 moves, ending with a 4 (yes, starting the third turn at 58, 60, 65, or indeed 77)




              So finally, the answer is




              It's Green's turn, and after that it's time for the fourth round, with Red playing next.







              share|improve this answer


























                up vote
                1
                down vote













                The other guys already got the answer (with possibly slightly dubious arguments), but the explanations are a bit hard to follow without pictures, so here's one:




                enter image description here




                Legend:



                • Red square: after turn 1, you are in one of these.

                • Green square: after turn 2, you are in one of these, or in some red square.

                • Red circle with R: if Red was the last player to move, Red's turn started at one of these.

                From there, the solution is pretty simple:




                1. Green has had either one or two turns.

                2. Therefore, Red has had at most three turns.

                3. Therefore, because no green square overlaps with a letter R, Red was not the last to move.

                3.1 There is no way to get to Red's current position with 2 turns only, So Red has taken at least 3 turns. Combined with point 2, Red has taken exactly 3 turns.

                4. Therefore, Green has taken 2 turns, rolling first 1, then 2.




                So the only remaining things to check are that




                5. Red really can get to its current square in 3 turns (yes, starting the third turn at 66, 62, 60 or 56.)

                6. Blue can get to its current spot in 3 moves, ending with a 4 (yes, starting the third turn at 58, 60, 65, or indeed 77)




                So finally, the answer is




                It's Green's turn, and after that it's time for the fourth round, with Red playing next.







                share|improve this answer
























                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  The other guys already got the answer (with possibly slightly dubious arguments), but the explanations are a bit hard to follow without pictures, so here's one:




                  enter image description here




                  Legend:



                  • Red square: after turn 1, you are in one of these.

                  • Green square: after turn 2, you are in one of these, or in some red square.

                  • Red circle with R: if Red was the last player to move, Red's turn started at one of these.

                  From there, the solution is pretty simple:




                  1. Green has had either one or two turns.

                  2. Therefore, Red has had at most three turns.

                  3. Therefore, because no green square overlaps with a letter R, Red was not the last to move.

                  3.1 There is no way to get to Red's current position with 2 turns only, So Red has taken at least 3 turns. Combined with point 2, Red has taken exactly 3 turns.

                  4. Therefore, Green has taken 2 turns, rolling first 1, then 2.




                  So the only remaining things to check are that




                  5. Red really can get to its current square in 3 turns (yes, starting the third turn at 66, 62, 60 or 56.)

                  6. Blue can get to its current spot in 3 moves, ending with a 4 (yes, starting the third turn at 58, 60, 65, or indeed 77)




                  So finally, the answer is




                  It's Green's turn, and after that it's time for the fourth round, with Red playing next.







                  share|improve this answer














                  The other guys already got the answer (with possibly slightly dubious arguments), but the explanations are a bit hard to follow without pictures, so here's one:




                  enter image description here




                  Legend:



                  • Red square: after turn 1, you are in one of these.

                  • Green square: after turn 2, you are in one of these, or in some red square.

                  • Red circle with R: if Red was the last player to move, Red's turn started at one of these.

                  From there, the solution is pretty simple:




                  1. Green has had either one or two turns.

                  2. Therefore, Red has had at most three turns.

                  3. Therefore, because no green square overlaps with a letter R, Red was not the last to move.

                  3.1 There is no way to get to Red's current position with 2 turns only, So Red has taken at least 3 turns. Combined with point 2, Red has taken exactly 3 turns.

                  4. Therefore, Green has taken 2 turns, rolling first 1, then 2.




                  So the only remaining things to check are that




                  5. Red really can get to its current square in 3 turns (yes, starting the third turn at 66, 62, 60 or 56.)

                  6. Blue can get to its current spot in 3 moves, ending with a 4 (yes, starting the third turn at 58, 60, 65, or indeed 77)




                  So finally, the answer is




                  It's Green's turn, and after that it's time for the fourth round, with Red playing next.








                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 6 mins ago

























                  answered 37 mins ago









                  Bass

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