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Classic Sam Loyd Tongue Twister on Multiplication (perplexed professor)

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Tommy muttonhead propounds to his teacher the perplexing query: "If five times six were 33, what would the half of 20 be?" The other pupils solved the problem redily, but Tommy could not see how a thing that was not what they said it was had anything to do with something else that is not what they say it is.

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half of 20 would still be written 10, if it's going the same direction I think it is, which is different numerical bases.



Regardless of base, 20 means 2 times the base. Therefore, half of 20 is 1 times the base, 10.

5x6=33 in base 9, by the way.

Let x represent the base number; then 30 in base ten is equal to 3x+3

30=3x+3, 10=x+1, x=9

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