"You again?" said the owner of the old curiosity shop. "Considering what you sold me last time, I'm surprised that you dare show your face in here."
"It wasn't my fault that the statues corroded to dust if polished after midnight," protested Colorado Smith. "Anyway, what I've brought you this time will pay for your losses and leave you a handsome profit." He placed five gold statues on the counter.
"These look exactly the same as the last ones," said the elderly Chinese shopkeeper.
"Ah, but these really are gold. Here's proof from the assay office. Um—again I don't know what they weigh. But I do know that they all have different weights."
"I will need to place them in order of weight," said the shopkeeper. "And I still have not recovered my stolen weights, so all I have is my balance. I could compare them in my hands, but some may be very close to others and I may get the order wrong."
"The pans will hold only one statue each," Smith observed.
"I can see how to do it with ten comparisons," said the old man, "comparing each with the previously compared ones."
"Unfortunately these objects cannot be compared more than seven times."
"Why not?"
"An ancient curse. You don't want to know." Smith put on his most engaging grin. "Trust me. You'll get more than you barg—I mean, you'll get a real bargain."
How can the shopkeeper place the weights of the statues in order?
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The answer
All five statues have different weights.
(1) Weigh two of them. Call the lighter one A and other B.
(2) Weigh two more. Call the lighter one C and other D.
(3) Weigh B against D. If D is lighter than B, swap the names of the pairs A, B and C, D. We now know that D>B>A.
(4) Call the last statue E and weigh it against B. If E is heavier than B, then;
(5a) compare E with D. If E is lighter than B, then;
(5b) compare E with A. We have now ranked four statues. Rename them U, V, W, X so that U>V>W>X.
(6) Compare C with W. If C is heavier than W then;
(7a) compare C with V. (We know C (7b) compare C with X.
The winner was Mike Brown from Hants
