### Brain Teasers

# Some Squares

You are a 3rd grader. You have been victorious during the food fight today in school. As you walk home, a 5th grader suddenly jumps up behind you, with some moldy food from last week in his hand. He threatens to splat you unless you answer the following question correctly in 10 seconds:

What is the square of 11,111,111?

What is the square of 11,111,111?

### Hint

The 5th grader looks down at you, and says, "I'll give you one hint: The square of 111 is 12,321."### Answer

123,456,787,654,321Using the hint, and the fact that the squares of 1 and 11 are 1 and 121, respectively, we can see a pattern in the series. When all the digits of a number are 1, and there are under 10 digits, the square of the number is 123...n...321, where n is the number of digits in the original number. Note however that this pattern only works for numbers with less that 10 digits, and all the digits must be 1.

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