CAS Musings

So here’s another musing I had on a beach visit. I don’t recall where I learned this trick, but I’ve had it for decades.  I suspect most of you already know how you can multiply by 9 using your fingers, but I’ll briefly explain just in case.  An extension follows.

Start by laying out both hands with all fingers outstretched.  Number your fingers from 1 to 10 from left to right.

To compute $latex 9*n$ for integer values of $latex n$ between 1 and 10, fold down the $latex n^{th}$ finger and count the number of still-extended fingers before and after the folded finger. Thinking of those two numbers as a two-digit number gives your answer. For example, to compute $latex 9*9$, fold down the $latex 9^{th}$ finger as shown below.

Because there are 8 fingers before the fold and 1 after, $latex 9*9=81$. Simple.

On the beach, I recalled…

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