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CryptoMath: 7 - 9 = 8? or 3 + 3 + 3 = 7?

Every letter in the following problems represents a different digit from 0 to 9. It is possible to discover what the digits are to make these equations true.

  • Problem 1: SEVEN - NINE = EIGHT
  • Problem 2: HAPPY + HAPPY + HAPPY + DAYS = AHEAD
  • Problem 3: THREE + THREE + THREE = SEVEN
Can you discover more than one solution for each problem?

If you found a solution, can you prove that it is the only possible solution for that problem?

 

Source: H.V. (Bellingham)


Hint: To get started on the first one, we can expect S = E+1...then focus on possibilities for N-E = T. What if a "borrow" is involved?

And for the third problem, is it easier to rewrite it in the form of THREE x 3 = SEVEN?

 


Solution Commentary: When submitting this problem, the mathematics teacher (H.V.) adds that "they can test a student's problem solving techniques. Each problem can be attacked in a different way and some problems have more than one solution. Some students may just use trial and error while others may be more systematic possibly using algebra equations....An extension might be for two or more students to get together, make up their own problems, and solve each others.What difficulties are there in doing this? Is there only one solution?"

Some possible answers:

  • 54146 - 6764 = 47382
  • 29661 + 29661 + 29661 + 3910 = 92893
  • 23199 + 23199 + 23199 = 69597