A woman wants to buy something at an auction where you bid grams of gold instead of money. She owns a length of gold chain (with 2 ends) 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?
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