It was stocktaking time at Amanda's Beautique, and the owner had found a problem with her mix-'n'-match bikinis.
"I thought we had three left," Amanda said to her assistant Camilla. "One with a red top and red bottom, one with a blue top and blue bottom, and one with one half red and the other half blue."
"We do," said Camilla. "They're in those three boxes behind the water cooler."
"I want the all-red bikini," said Amanda, pulling out the boxes. "Oh, good, they're labelled. One says RR, one says BB, and one says RB. I suppose—"
"Er, actually," said Camilla. "I'm afraid that all three labels are wrong. Sorry."
"Can you remember which is which?
"No."
Amanda looked at the boxes, which were heavily taped. "It'll take ages to open them."
"It's worse than that," said Camilla. "Inside, each piece of the bikini is separately wrapped inside a thick opaque plastic bag. Both bags look identical. And the bags are heavily taped, too."
"Oh Lord," said Amanda. "All I want is to find the right box. I don't need to open it. I wonder what's the best way to find out."
What is the smallest number of boxes that Amanda needs to open, and how many of the bags inside it should she unwrap?
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The answer
One box and one bag is enough.
Amanda should open the box marked RB, and then open one of its bags. If the garment inside is red, then so must the other one be, since the RB label is wrong. Then the only possibility is that the BB box contains a red-blue pair, and the RR box contains an all-blue bikini. Alternatively, if the bag contains a blue garment, then so must the other one. Then the BB box contains an all-red bikini, and the RR box contains a red-blue pair.
The winner was Kay George, Cheshire
