FILE No.66Unsolved
A thief will stay at an inn for seven days. The price is one segment of a gold bar per day, paid that same day.
His gold bar is made of seven equal segments joined in a single row, and it can only be cut along the boundaries between segments. The innkeeper may also give pieces back as change.
So each day the thief may hand over some pieces and take back some he gave earlier, as long as the innkeeper holds exactly the right total.
What is the fewest number of cuts needed so he can pay correctly every day for seven days?
If you get stuck, open the hints one at a time, in order.
Each day the total held by the innkeeper must be 1, 2, 3, ..., 7.
Which set of pieces can make every number from 1 to 7?
Think of binary: 1, 2, 4.
What is the fewest number of cuts needed so he can pay correctly every day for seven days?
Choose the answer closest to the truth.
2 cuts
The answer is: 2 cuts.
Cut the bar into pieces of 1, 2 and 4 segments: first cut off 1 segment, then cut the remaining 6 into 2 and 4. That is two cuts.
Day 1: give 1. Day 2: give 2, take back 1. Day 3: give 1 and 2 (total 3). Day 4: give 4, take back 1 and 2. Day 5: give 4 and 1. Day 6: give 4 and 2, take back 1. Day 7: give all (total 7). Pieces of 1, 2, 4 can make every total from 1 to 7.
If you think of cutting one segment per day, it looks like you need six cuts.
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