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I am trying to create a puzzle using the prime numbers (from 1 to 50): $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47$ . No repeats allowed.

I want it to look like this:

http://oi63.tinypic.com/2wgvp60.jpg

The other operations can be filled in any way (either + or -). Just to clarify the totals must also be primes from the list.

If it helps, the 2 can be positioned somewhere else.

I have tried for several hours but I can't make one without using repeats or non primes.

If not possible, is it possible to make one using primes from 1-100 instead?

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  • $\begingroup$ Can you say anything about why you have the particular constraints you do? E.g., why multiplications rather than +/- in those two places? $\endgroup$
    – Gareth McCaughan ♦
    Commented Jan 11, 2018 at 23:02
  • $\begingroup$ I was making this puzzle so that BIDMAS would have been be used somewhere. And the only number this can apply with is the 2. I chose one to be before the 2 and one after. $\endgroup$
    – Bob
    Commented Jan 11, 2018 at 23:03
  • $\begingroup$ Only the numbers in the boxes need to be prime right? And not the ones outside the box? $\endgroup$
    – user44233
    Commented Jan 12, 2018 at 4:39
  • $\begingroup$ "The other operations can be filled in any way (either + or -)"; so the other operations are not multiplication? $\endgroup$
    – pizzapants184
    Commented Jan 12, 2018 at 20:50
  • $\begingroup$ The accepted answer does not have the '2' or operations listed in the image. If these are not required, please edit your question to make this clear. ('other operations' -> 'operations', etc.) $\endgroup$
    – pizzapants184
    Commented Jan 13, 2018 at 2:35

2 Answers 2

Reset to default
7
$\begingroup$ 
2  +  3 * 5  = 17
*     +   +
7  + 47 - 11 = 43
+     -   +
23 + 31 - 13 = 41
=     =   =
37   19   29



2  + 3  *  5 = 17
*    +     +
7  + 47 - 13 = 41
+    -     +
23 + 31 - 11 = 43
=    =    =
37   19   29
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3
  • $\begingroup$ Thank you. How did you find these? Trial and error or did you use some sort of program/code? $\endgroup$
    – Bob
    Commented Jan 12, 2018 at 17:09
  • $\begingroup$ I think it almost impossible to find it by hand, because there is no math formula to find it easily, so I use Haskell to find the solution. $\endgroup$
    – Jamal Senjaya
    Commented Jan 13, 2018 at 3:00
  • $\begingroup$ Which numbers should I include so that the puzzle is possible to solve without guessing? I was thinking the 3, 17, 23 and 19 - any more? $\endgroup$
    – Bob
    Commented Jan 14, 2018 at 1:27
1
$\begingroup$ 
 2 *  3 + 37 = 43
 *    +    -
 5 -  7 + 19 = 17
 +    +    +
13 - 31 + 29 = 11
 =    =    =
23   41   47

 2 *  3 + 37 = 43
 *    +    -
 5 - 41 + 47 = 11
 +    -    +
 7 - 13 + 29 = 23
 =    =    =
17   31   19

 2 *  3 + 37 = 43
 *    +    -
 5 - 41 + 47 = 11
 +    -    +
19 - 13 + 17 = 23
 =    =    =
29   31    7

etc.

These were generated with a python script available here (press run).

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6
  • $\begingroup$ How can I change the code so that I can find puzzles with more than one solution? What I mean is if I have a grid with the operations fixed then there's two possible answers e.g. the accepted answer. $\endgroup$
    – Bob
    Commented Jan 14, 2018 at 2:05
  • $\begingroup$ @Bob Here is a (probably rather inefficient) version of the script that generates filled-in squares, then find other numerical solutions with the same operations. Groups of same-operation-squares are preceded by the list of operators they use (horizontal right-down, then vertical down-right order). $\endgroup$
    – pizzapants184
    Commented Jan 14, 2018 at 3:40
  • $\begingroup$ Thanks. I ran the code for a while and saw it repeating some solutions. Can this be fixed? $\endgroup$
    – Bob
    Commented Jan 14, 2018 at 14:30
  • $\begingroup$ @Bob I updated the link in my other comment $\endgroup$
    – pizzapants184
    Commented Jan 14, 2018 at 20:39
  • $\begingroup$ I get the following error: Traceback (most recent call last): File "python", line 15 O,P,Q,R,S,T,U,V,W,X,Y,Z = op_list ^ TabError: inconsistent use of tabs and spaces in indentation $\endgroup$
    – Bob
    Commented Jan 14, 2018 at 21:45

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