Cut the chain riddle
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What is the least number of links you can cut in a chain of 21 links to be able to give someone all possible number of links up to 21? 
You need to cut 3 links.
After these cuts you have 3 pieces of length 2, 4, 8 and a remaining piece of length 4
And also 3 broken links (2+4+8+4+3×1 = 21)
With one broken link and the pieces of length 2, 4 and 8 we can count to 15 in binary.
For numbers above 15 we can use the remaining 6 links as an offset.
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