Do Nothing
Puzzle. How can you make the following equation correct without changing it: 8 + 8 = 91?
The intended answer: turn the paper over! When flipped upside down, the equation becomes 16 = 8 + 8.
As you might expect, my blog post doesn’t stop there. I’d like to share some creative ideas my students came up with when they tackled this puzzle as part of their homework.
The most common suggestion was to interpret the equation modulo some number. For example, it works modulo 75. By extension, it also works modulo any divisor of 75: 3, 5, 15, or 25.
They also suggested interpreting the equation in base 5/3.
One far-fetched but imaginative submission proposed the following: Suppose the equation is written in an alien language whose symbols look identical to ours but have different meanings. In this alien base-10 system, the symbols + and = mean the same as on Earth, but an 8 represents 6, a 9 represents 1, and a 1 represents 2. Then the alien equation 8 + 8 = 91 translates to 6 + 6 = 12 in human, which is perfectly true.
But my favorite answer was the following:
- Interpret the question mark as a variable and solve the equation. This gives ? = 16/91. We didn’t change the equation — just solved it!
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