think of a number that is less than 100. If you add 4 to my number you get a square number. If you subtract 5 from my number you get a cube number. Which number am I thinking of?
Question
think of a number that is less than 100. If you add 4 to my number you get a square number. If you subtract 5 from my number you get a cube number. Which number am I thinking of?
Solution
Let's solve this step by step:
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First, we need to find a number that when added by 4 results in a square number. Square numbers under 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. So, the possible numbers could be -3, 0, 5, 12, 21, 32, 45, 60, 77, 96.
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Next, we need to find a number that when subtracted by 5 results in a cube number. Cube numbers under 100 are 1, 8, 27, 64. So, the possible numbers could be 6, 13, 32, 69.
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The number that satisfies both conditions is 32. When you add 4 to 32, you get 36 which is a square number (66). When you subtract 5 from 32, you get 27 which is a cube number (33*3).
So, the number you are thinking of is 32.
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