Adela’s math puzzle

Time to brag on my 7-year-old. Adela has been thinking up math problems for me each night. Tonight it was the following. Start with a number, say 2, and do all four operations on it: 2+2=4, 2*2 = 4, 2-2 = 0, and 2/2 = 1. Now add the results all up, getting 4+4+1+0=9.

If you start with 3, you get 3+3=6, 3*3 = 9, 3-3 = 0, and 3/3 = 1. Adding gives 6+9+1+0=16. Hmm…I think I see a pattern here….

Starting with 4 gets you 8+16+1+0=25, which is 5^2 = (4+1)^2.

Of course this is just a cute way of saying that (n+1)^2 = n^2 + 2*n + 1, or more explicitly

(n+1)^2 = n*n + (n+n) + n/n + (n-n)

which I don’t think I had ever thought of in exactly that way. Hurray for kids!

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