December 2009
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The product is even, so it must be a power of 2, which means that every one of the 10 terms has only one bit set. The condition actually implies that x encodes a permutation on 5 elements. N=7 questions are needed and, for example, the N-2=5 mask questions {0x83, 0x700, 0x41800, 0x288000, 0xc00010} divide the 120 possibilities into subsets of no more than 4 elements. It is easy to show that 2 more questions suffice.
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