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THERE ARE ONLY TWO NUMBERS WITH THE PROPERTY THAT EVERY DIGIT EXCEPT 0 APPEARS JUST ONCE IN THE NUMBER AND IT'S SQUARE WHAT ARE THE TWO NUMBERS?

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The two numbers that meet the criteria of having every digit except 0 appearing just once in the number and in its square are 1 and 76.

  1. 1:

    • The square of 1 is \(1^2 = 1\). The only digit is 1, which meets the requirement.

  2. 76:

    • The square of 76 is \(76^2 = 5776\). The digits in 76 are 7 and 6, appearing once each. In 5776, the digits 5, 7, and 6 also satisfy the condition (0 is excluded).

No other two-digit or three-digit numbers seem to fit this property based on the constraints you provided.