Consider this puzzle:

Number game

The answer given by the website is 10 (filled-in already in the picture) But I can't figure out why this is the case. My various thought processes so far have been:

  • The smaller the first number is, the bigger the second number is
  • The smaller numbers here appear to be factors of the bigger numbers, but they don't appear in any definite order
  • The differences between opposite numbers are prime (37, 19, 7, 2), but they don't follow any sequence, even if one was to try and guess hypothetical other pairs.

Has anyone seen this puzzle before? Can you explain how you justify the answer?

Context: My little brother is in grade 5 of his Australian schooling and is practicing for the upcoming NAPLAN tests, when going through the answers with him, I couldn't explain why the answer is what it is for this puzzle, which is why I've sought out advice here.


All opposite no. when multiplied give $120$. Get it. :D

$8*15=3*40=24*5=12*x=120\implies x=10$

  • $\begingroup$ Thank you! I was hoping it would be something simple. Well done $\endgroup$ – Siberias May 12 '14 at 2:28

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