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Aliens have been found in Mars who have six fingers in each of their hands, total $12$ fingers in their two hands. We use $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ to do all the calculation, and they use $0, 1, 2, 3, 4, a, 5, 6, 7, 8, 9, b.$ So, $10, 11, 12$ in earth is $9, b, 10$ in Mars. Find the product of $1b$ and $16$ in aliens’ system.

Attempt:

We use the symbol $A$ to denote the alien numbers. I found that $(1b)_A = 23$ and $(16)_A = 19$, but how do we find the product in base $A$?

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    $(1b)_A$ is very far from $(155)_E$. – 2017-01-18
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    1b is 1(11), not 110. ie. is is 1x12 + b = 1x12 + 11. It isn't 1x12^2 + 1x12 + 0 by any means. That "10" that you write need to be considered as a single digit.. Not two.... or... you could not 1b = 20 -1. So 1b = 23. – 2017-01-18
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    Okay... I actually don't understand why you think $1b_A = 110_A - 1$. I don't see it at all. Don't you mean $1b_A = 20_A - 1$? – 2017-01-18
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    ..also you got 2945 in earth. You need to convert it back to alien. – 2017-01-18

1 Answers 1

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$$(1b)_A=12+11$$ $$(16)_A=12+7$$

\begin{align}(12+11)(12+7)&=12^2+18 \times 12+ 77\\ &= 12^2+18 \times 12+ 6 \times 12 + 5\\ &= 12^2+24\times 12+5\\ &= 12^2+2 \times 12^2 +5 \\ & = 3 \times 12^2+5\\ &=(30a)_A \end{align}

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    Nice answer. I'm *really* happy you did not convert alien to english, do the math, and convert back to alien. – 2017-01-18