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Break the Chain

A woman wants to buy a painting at an auction where you bid grams of gold instead of money. She owns a gold chain made of 23 interlocking loops, each weighing 1 gram. She wants to go to a jeweler before the auction to cut the minimum number of loops that would allow her to pay any sum from 1 to 23. For example, she could pay a 13 gram price with a 12 link chain and a single link. After much thought, she figures out a way to do it by cutting just 2 of the loops in the chain. How many loops are in the pieces of chains that she has after the 2 cuts?

SOLUTION : Cut the fourth and eleventh loops and separate them. So, the chain gets divided into 5 parts of 3 loops, 1 loop, 6 loops, 1 loop and 12 loops. Using these 5 pieces, any sum from 1 to 23 loops can be paid. You can yourself work out this thing. Believe us, it is very easy.

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