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your finger can provide an (n-1) multiplication table in base n, 2 ? n ? 10 , as follows: To multiply (n-1) by k in base n, lower the k th finger from the left while holding up n fingers. Your answer is (a*b) n or (b) n if a = 0, where a*b is a string, a is the number of fingers to the left of the finger you lowered and b is the number of fingers to the right. Explain why this works without listing all possible cases. Solution let the number of fingers holding up be n... let the kth finger from left be lowered.. now number of fingers holding up on the left is (k-1) and number of fingers holding up on the right is (n-k). now it is said that [(k-1)*(n-k)]_n string is the product of (n-1) and k in base n. this can checked by writing [(k-1)*(n-k)]_n in base n which is (k-1)n+(n-k)=kn-k=(n-1)k which is precisely the product of n-1 and k in base n. .

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