Nob’s Number Tree

Nob's Number Tree
Nob’s Number Tree

What number belongs in the “?” circle? Note that all numbers shown are correct, there are no typos or errors.

Nob Yoshigahara’s Puzzles

Nob’s Number Tree is a well-known brainteaser by the Japanese puzzle guru Nobuyuki “Nob” Yoshigahara, who wrote many mathematical puzzle books and invented many puzzle toys. This cheeky number tree puzzle seems straightforward, but the straightforward solution falls apart when you arrive at the bottom.

Click to see solution

The answer is 12.

You get this by adding up all the digits in a row to get the number in the circle below. For example, 7 + 2 + 9 + 9 = 27 for the first row. So 2 + 1 + 3 + 6 = 12.

If you thought the solution was 15, you may have fell for Nob’s cleverly-laid trap! 15 unfortunately is not a valid solution.

See, it appears that you can just take the difference between the two numbers in a row to arrive at the number in the circle below (for example, 99 – 72 = 27). However, this pattern works for most of the rows but does not work for the last row (21 – 13 ≠ 7), and you were told that there were no typos or errors.

However, 2 + 1 + 1 + 3 = 7, which confirms adding the digits is correct, and taking the difference is incorrect.

The puzzle is devious in that Nob selected numbers such that they lead you down the path of an obvious solution – only to dispel the illusion at the end. Many are convinced the last number is an error, until the solution is shown to be simple and straightforward as well.

Liked this Nob Yoshigahara puzzle?
He also designed physical puzzles!
Hanayama News Puzzle by Nob Yoshigahara

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    • Nob’s puzzle is clever in that it tries to trick you into thinking 15 is a solution, but unfortunately it actually doesn’t work!

      I have expanded the explanation to make it clearer why 15 does not work.

    • That’s part of the fun of this puzzle. Unfortunately, the last line shows this method doesn’t work, because 21-13≠7. Click on the solution above to see the full explanation.

  1. Simply if you add the two numbers in each circle the arrow points to the sum of both circles, so I would consider both circles as parentheses that are added to itself internally and then added to by both sums.

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