The 1-expression

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A 1-expression is a formula in which you add or multiply the number 1; in addition, parentheses are also allowed.
You can create any natural number with a 1 expression.



For example, 22 as follows:
1 + 1 + ((1 + 1 + 1 + 1) × (1 + 1 + 1 + 1 + 1)) = 22
This is a 1-expression with 11 times a 1 in it.



You could also have done:
1 + ((1 + 1 + 1) × (1 + ((1 + 1) × (1 + 1 + 1)))) = 22
This is a 1-expression with only 10 times a 1 in it. 10 is the minimum 1 value of 22, that is that there is no 1-expression with which you can make 22 where you use a 1 less than 10 times.
Your task is to determine the minimum 1 value of 73.






mathematics







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  • Is concatenating allowed (e.g. combining 2 1s to form an 11)?
    – Excited Raichu
    30 mins ago











  • @ExcitedRaichu I'd assume not or else the minimum 1s for the example with 22 would be 4 instead of 10, (11 +11)
    – gabbo1092
    27 mins ago










  • @gabbo1092 oh right lol
    – Excited Raichu
    26 mins ago














up vote
3
down vote

favorite












A 1-expression is a formula in which you add or multiply the number 1; in addition, parentheses are also allowed.
You can create any natural number with a 1 expression.



For example, 22 as follows:
1 + 1 + ((1 + 1 + 1 + 1) × (1 + 1 + 1 + 1 + 1)) = 22
This is a 1-expression with 11 times a 1 in it.



You could also have done:
1 + ((1 + 1 + 1) × (1 + ((1 + 1) × (1 + 1 + 1)))) = 22
This is a 1-expression with only 10 times a 1 in it. 10 is the minimum 1 value of 22, that is that there is no 1-expression with which you can make 22 where you use a 1 less than 10 times.
Your task is to determine the minimum 1 value of 73.






mathematics







share|improve this question







New contributor




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



















  • Is concatenating allowed (e.g. combining 2 1s to form an 11)?
    – Excited Raichu
    30 mins ago











  • @ExcitedRaichu I'd assume not or else the minimum 1s for the example with 22 would be 4 instead of 10, (11 +11)
    – gabbo1092
    27 mins ago










  • @gabbo1092 oh right lol
    – Excited Raichu
    26 mins ago












up vote
3
down vote

favorite









up vote
3
down vote

favorite











A 1-expression is a formula in which you add or multiply the number 1; in addition, parentheses are also allowed.
You can create any natural number with a 1 expression.



For example, 22 as follows:
1 + 1 + ((1 + 1 + 1 + 1) × (1 + 1 + 1 + 1 + 1)) = 22
This is a 1-expression with 11 times a 1 in it.



You could also have done:
1 + ((1 + 1 + 1) × (1 + ((1 + 1) × (1 + 1 + 1)))) = 22
This is a 1-expression with only 10 times a 1 in it. 10 is the minimum 1 value of 22, that is that there is no 1-expression with which you can make 22 where you use a 1 less than 10 times.
Your task is to determine the minimum 1 value of 73.






mathematics







share|improve this question







New contributor




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











A 1-expression is a formula in which you add or multiply the number 1; in addition, parentheses are also allowed.
You can create any natural number with a 1 expression.



For example, 22 as follows:
1 + 1 + ((1 + 1 + 1 + 1) × (1 + 1 + 1 + 1 + 1)) = 22
This is a 1-expression with 11 times a 1 in it.



You could also have done:
1 + ((1 + 1 + 1) × (1 + ((1 + 1) × (1 + 1 + 1)))) = 22
This is a 1-expression with only 10 times a 1 in it. 10 is the minimum 1 value of 22, that is that there is no 1-expression with which you can make 22 where you use a 1 less than 10 times.
Your task is to determine the minimum 1 value of 73.






mathematics




mathematics






share|improve this question







New contributor




Noah 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 question







New contributor




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Check out our Code of Conduct.









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asked 31 mins ago









Noah

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182




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New contributor





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






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











  • Is concatenating allowed (e.g. combining 2 1s to form an 11)?
    – Excited Raichu
    30 mins ago











  • @ExcitedRaichu I'd assume not or else the minimum 1s for the example with 22 would be 4 instead of 10, (11 +11)
    – gabbo1092
    27 mins ago










  • @gabbo1092 oh right lol
    – Excited Raichu
    26 mins ago
















  • Is concatenating allowed (e.g. combining 2 1s to form an 11)?
    – Excited Raichu
    30 mins ago











  • @ExcitedRaichu I'd assume not or else the minimum 1s for the example with 22 would be 4 instead of 10, (11 +11)
    – gabbo1092
    27 mins ago










  • @gabbo1092 oh right lol
    – Excited Raichu
    26 mins ago















Is concatenating allowed (e.g. combining 2 1s to form an 11)?
– Excited Raichu
30 mins ago





Is concatenating allowed (e.g. combining 2 1s to form an 11)?
– Excited Raichu
30 mins ago













@ExcitedRaichu I'd assume not or else the minimum 1s for the example with 22 would be 4 instead of 10, (11 +11)
– gabbo1092
27 mins ago




@ExcitedRaichu I'd assume not or else the minimum 1s for the example with 22 would be 4 instead of 10, (11 +11)
– gabbo1092
27 mins ago












@gabbo1092 oh right lol
– Excited Raichu
26 mins ago




@gabbo1092 oh right lol
– Excited Raichu
26 mins ago










2 Answers
2






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up vote
4
down vote



accepted










I may as well throw this out there:




$((1 + 1)*(1+1)*(1+1)*(1+1+1)*(1+1+1))+1$, for a total of 13 ones.

This was accomplished by multiplying together the prime factors of 72, and adding one.







share|improve this answer





























    up vote
    1
    down vote













    I got this:




    $$(1+1)times(1+1)times(1+1)times(1+1+1)times(1+1+1)+1 = 73$$
    The minimum 1 value of 73 is 13







    share|improve this answer
















    • 1




      Sadly, Hugh was 10 seconds quicker...
      – Keelhaul
      20 mins ago






    • 1




      Good job though. I guess we both went for the prime-factor-plus-one route.
      – Hugh
      18 mins ago










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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    4
    down vote



    accepted










    I may as well throw this out there:




    $((1 + 1)*(1+1)*(1+1)*(1+1+1)*(1+1+1))+1$, for a total of 13 ones.

    This was accomplished by multiplying together the prime factors of 72, and adding one.







    share|improve this answer


























      up vote
      4
      down vote



      accepted










      I may as well throw this out there:




      $((1 + 1)*(1+1)*(1+1)*(1+1+1)*(1+1+1))+1$, for a total of 13 ones.

      This was accomplished by multiplying together the prime factors of 72, and adding one.







      share|improve this answer
























        up vote
        4
        down vote



        accepted







        up vote
        4
        down vote



        accepted






        I may as well throw this out there:




        $((1 + 1)*(1+1)*(1+1)*(1+1+1)*(1+1+1))+1$, for a total of 13 ones.

        This was accomplished by multiplying together the prime factors of 72, and adding one.







        share|improve this answer














        I may as well throw this out there:




        $((1 + 1)*(1+1)*(1+1)*(1+1+1)*(1+1+1))+1$, for a total of 13 ones.

        This was accomplished by multiplying together the prime factors of 72, and adding one.








        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 9 mins ago

























        answered 22 mins ago









        Hugh

        674410




        674410




















            up vote
            1
            down vote













            I got this:




            $$(1+1)times(1+1)times(1+1)times(1+1+1)times(1+1+1)+1 = 73$$
            The minimum 1 value of 73 is 13







            share|improve this answer
















            • 1




              Sadly, Hugh was 10 seconds quicker...
              – Keelhaul
              20 mins ago






            • 1




              Good job though. I guess we both went for the prime-factor-plus-one route.
              – Hugh
              18 mins ago














            up vote
            1
            down vote













            I got this:




            $$(1+1)times(1+1)times(1+1)times(1+1+1)times(1+1+1)+1 = 73$$
            The minimum 1 value of 73 is 13







            share|improve this answer
















            • 1




              Sadly, Hugh was 10 seconds quicker...
              – Keelhaul
              20 mins ago






            • 1




              Good job though. I guess we both went for the prime-factor-plus-one route.
              – Hugh
              18 mins ago












            up vote
            1
            down vote










            up vote
            1
            down vote









            I got this:




            $$(1+1)times(1+1)times(1+1)times(1+1+1)times(1+1+1)+1 = 73$$
            The minimum 1 value of 73 is 13







            share|improve this answer












            I got this:




            $$(1+1)times(1+1)times(1+1)times(1+1+1)times(1+1+1)+1 = 73$$
            The minimum 1 value of 73 is 13








            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 21 mins ago









            Keelhaul

            7,2582473




            7,2582473







            • 1




              Sadly, Hugh was 10 seconds quicker...
              – Keelhaul
              20 mins ago






            • 1




              Good job though. I guess we both went for the prime-factor-plus-one route.
              – Hugh
              18 mins ago












            • 1




              Sadly, Hugh was 10 seconds quicker...
              – Keelhaul
              20 mins ago






            • 1




              Good job though. I guess we both went for the prime-factor-plus-one route.
              – Hugh
              18 mins ago







            1




            1




            Sadly, Hugh was 10 seconds quicker...
            – Keelhaul
            20 mins ago




            Sadly, Hugh was 10 seconds quicker...
            – Keelhaul
            20 mins ago




            1




            1




            Good job though. I guess we both went for the prime-factor-plus-one route.
            – Hugh
            18 mins ago




            Good job though. I guess we both went for the prime-factor-plus-one route.
            – Hugh
            18 mins ago










            Noah is a new contributor. Be nice, and check out our Code of Conduct.









             

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