Can You Solve This Problem That Not Even Computers Understand?

This brainteaser is sometimes offered to people on computer courses — it’s possible for human beings to resolve, but no machine can ever work it out. Here it is:

How old are these 3 sisters, if:

  • Multiplying their ages gives a figure of 36;
  • Adding their ages together gives 13;
  • The oldest sister is blonde.

So did you work it out?

If multiplying their ages gives 36, then their ages have to be one of the following eight combinations:

36 = 2 × 3 × 6, and adding these ages together gives us 11.

36 = 2 × 2 × 9, and adding these ages together gives us 13.

36 = 4 × 9 × 1, and adding these ages together gives us 14.

36 = 4 × 3 × 3, and adding these ages together gives us 10.

36 = 18 × 2 × 1, and adding these ages together gives us 21.

36 = 12 × 3 × 1, and adding these ages together gives us 16.

36 = 6 × 6 × 1, and adding these ages together gives us 13.

36 = 36 × 1 × 1, and adding these ages together gives us 38.

We are left with two possible answers, since 2 + 2 + 9 = 13, as does 6 + 6 + 1. This is where the seemingly useless comment that “the oldest sister is blonde” turns out to be useful. This statement indicates that there is an older sister who doesn’t have a twin. In turn, only the first equation fits. Therefore, the answer is that the oldest sister is 9 years old and the younger ones are both 2.

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