## My Equation

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Here is an equation that I made up:

y=x^5-10x^4+35x^3-50x^2+25x

Here are some of the x and y values:

x   y
0   0
1   1
2   2
3   3
4   4

Can you predict what y is when x is 5?

Answer: Looking at the equation, you should know better than to answer 5. The answer is 125.

Here is a graph of the equation, drawn by Geometer's Sketchpad.

If I had merely given you the table, and not the equation, you would have been justified in guessing 5. But, you should have recognized that the equation cannot be the equation of a straight line. But, having seen this example, perhaps you should be wary every time you are asked to name the next number in a sequence. The puzzle books are looking for the simplest such sequence. But there are infinitely many (more complicated) sequences which fit their data.