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You have probably heard of code golfing? There the task is to find the shortest computer program that produces the required output. Here we want to perform math golfing - find the shortest formula that produces a given number. The length of a formula is measured as the number of characters. The format must be as follows:

  • Contain only digits '0' to '9' and characters '+' (addition), '-' (subtraction), '*' (multiplication), '^' (exponentiation), brackets '(' and ')'.
  • Digits can be concatenated such as 567.
  • Operations have precedence, like in BODMAS. Brackets are done first, followed by exponentiation, followed by multiplication, followed by addition/subtraction (from left to right).
  • For example (10^2+1)*2^5 is equivalent to (100+1)*32 = 3232. The formula uses 12 characters, so it is not a compact representation of the result that has 4 characters.

Find the shortest formulas that represent the following numbers:

  1. 99999999999
  2. 41601569625
  3. 61917364165
  4. 82644187136
  5. 33059881770
  6. 12345678901234
  7. 10101010101010
  8. 33333333333333
  9. 68945723674934237482
  10. 5782934283492912347898237400000
  11. 34828517376
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  • $\begingroup$ Partial answers are accepted too! $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 3, 2020 at 4:49
  • 1
    $\begingroup$ "from left to right" breaks the default priority of $a^{b^c} = a^{(b^c)}$, though. $\endgroup$
    – the default.
    Commented Jun 3, 2020 at 5:42
  • $\begingroup$ Is a unary minus allowed? $\endgroup$
    – Jens
    Commented Jun 4, 2020 at 19:48
  • $\begingroup$ Jens yeah why not. Any attempts at the missing numbers? $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 5, 2020 at 0:48
  • $\begingroup$ I have decided to add brackets to make things a bit more interesting, especially for those larger terms. The current answer is still valid. $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 5, 2020 at 2:26

1 Answer 1

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I'm still missing a few of the answers.

99999999999 = (7 characters)

10^11-1

41601569625 = (6 characters)

3465^3

61917364165 = (8 characters)

12^10-59

82644187136 = (6 characters)

4*14^9

33059881770 = (9 characters)

3*18^8+42

12345678901234 = ?

10101010101010 = ?

33333333333333 = ?
I had an 11-character solution but that used division (10^14/3-1/3).

68945723674934237482 = ?

5782934283492912347898237400000 = ?

34828517376 = (5 characters, Thanks to Ben J in the comments)

432^4

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  • $\begingroup$ Very nice Jaap! You have matched my best results and improved some of them. $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 3, 2020 at 6:18
  • 1
    $\begingroup$ For the last number, it's possible to golf another 2 characters by rearranging to remove an operator. $\endgroup$
    – Tobbs
    Commented Jun 4, 2020 at 15:11
  • $\begingroup$ Great observation Ben! $\endgroup$
    – Dmitry Kamenetsky
    Commented Jun 5, 2020 at 0:47

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