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.

You might have been misled to think the pattern was taking the difference between the two numbers in a row to get the number in the circle below (for example, 99 – 72 = 27). This pattern works for most of the rows but breaks down 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.


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