### Brain Teasers

# The Really Really Big Number

Letter-Equations
Letter Equations are well known phrases or facts where the key words have been replaced with the first letter of that word. These are often in the form of an equation, which contain a number, an = sign and the rest of the obscured phrase or fact.

When you divide 12 by 5, the remainder is 2; it's what's left over after you have removed all the 5s from the 12. When you raise 4 to the fifth power (that is, 4^5), you multiply four by itself five times: 4x4x4x4x4, which equals 1,024.

What is the remainder when you divide 100^100 by 11?

What is the remainder when you divide 100^100 by 11?

### Answer

1This one is so sneaky.

First, consider 100 divided by 11. The remainder here is 1. Now consider the remainder when 100x100 is divided by 11. Don't do it on your calculator or on paper. Rather, consider that you have one hundred hundreds, and each of them has a remainder of 1 when divided by 11. So, go through each of your hundred hundreds and divide it by 11, leaving remainder 1. Then collect up your remainders into a single hundred, and divide it by 11, leaving a remainder of 1. This process can be extended to dividing 100x100x100 by 11, and indeed, to dividing any power of 100 by 11.

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