Unfinished Snakes and Ladders
Clash Royale CLAN TAG#URR8PPP
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?
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
add a comment |Â
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?
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
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
add a comment |Â
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?
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
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?
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
board-games retrograde-analysis
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
add a comment |Â
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
add a comment |Â
3 Answers
3
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.
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
add a comment |Â
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.
add a comment |Â
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:
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.
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
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.
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
add a comment |Â
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.
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
add a comment |Â
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.
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.
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.
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
add a comment |Â
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
add a comment |Â
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.
add a comment |Â
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.
add a comment |Â
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.
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.
answered 3 hours ago
ImongMama
1415
1415
add a comment |Â
add a comment |Â
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:
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.
add a comment |Â
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:
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.
add a comment |Â
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:
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.
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:
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.
edited 6 mins ago
answered 37 mins ago
Bass
23.8k458153
23.8k458153
add a comment |Â
add a comment |Â
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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