Q: How many 2 digit numbers have digits whose sum is a perfect square?

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12689 14689 12489

I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.

With 123 digits you can make 123 one-digit numbers.

Six: 0, 1, 4, 5, 6 and 9

The biggest number with 6 digits that is a perfect square is 999,999. When squared, it becomes 999,999,000,001.

Related questions

69

If the number with the digits reversed can have a leading 0 so that it is a 1-digit number, then 16. Otherwise 13.

102 = 100 which is the first possible three digit number that is a perfect square. 312 = 961 which is the last possible three digit number that is a perfect square. So there are 22 three digit positive numbers that are perfect squares.

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12689 14689 12489

I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.

4,624 = 682

With 123 digits you can make 123 one-digit numbers.

There are a lot of possibilities. The second digit can be 2 through 6, the third digit can be 3 through 7 as long as it is larger than the second digit. What we have so far: 1 _ _ 89

There are 5460 five digit numbers with a digit sum of 22.

Six: 0, 1, 4, 5, 6 and 9

The biggest number with 6 digits that is a perfect square is 999,999. When squared, it becomes 999,999,000,001.