XOR simplification

There are three integers a a , b b and c c . Given that

a b = 239 b c = 899 \begin{aligned} a \oplus b &=& 239 \\ b \oplus c &=& 899\end{aligned}

where \oplus is defined to be bitwise XOR on integers.

What additional information is required to recover all three of a a , b b and c c ?

Any one of a a , b b or c c Any one of a a or c c Only b b No additional information is required

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1 solution

Hasmik Garyaka
Sep 17, 2017

Adding given equation a xor c=876. There are infinite number of a,b,c satisfying this equations, because if we have 1 triplet, we can switch binary digit of all numbers and get another triplet. But if we know a, xoring it with first will give us b, and then c from the second. If we know b, xor it with 1 and 2 and get a and c immediatly.

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