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## Numbers are Special!

Think about the numbers 26, 40, 67, 77, 162, or 7807. Why are these numbers special? In fact, according to Eric Freidman's web site What's Special About This Number?, almost every number up to 9999 is special. For example, did you know the following:

• 26 is the only number that lies directly between a perfect square and a perfect cube
• 40 is the only number whose letters are in alphabetical order
• 67 is the smallest number which is palindromic in bases 5 and 6
• 77 is the largest number that can't be written as a sum of distinct numbers whose reciprocals sum to 1
• 162 is the smallest number that can be written as the sum of of 4 positive squares in 9 ways
• 7807 is the maximum number of regions a circle can be cut into with 36 cuts

I know...all of these properties were all on the tip of your tongue!

Admittedly, some of the special attributes are a "reach." For example, 102 is the smallest number with three different digits. Wow...that number 102 is special after all!

But, the web site is fascinating......plus you (and your students) can learn alot about properties of numbers and numbers with special names: Catalan numbers, Kaprekar numbers, Motzkin numbers, Smith numbers, Cullen numbers, Keith numbers, tetranacci numbers, and hyperfactorials.

And if you have the time and inclination, try to find a better special attribute for the number 102...and send it to Eric Friedman, a Mathematics Professor at Stetson university!