Cutting the Log
Read the puzzle
A single log must be cut into 5 pieces. Each cut takes 2 minutes and makes one break, turning 1 piece into 2. The rules say one cut at a time and no stacking pieces to cut them together. How long does it take to cut the log into 5 pieces?
How long to cut the log into 5 pieces?
How many cuts make 5 pieces?
8 minutes
5 pieces need only 4 cuts: 4 × 2 = 8 minutes.
How to solve it
Count cuts, not pieces. Each cut splits one piece into two, so every cut adds exactly one piece to the total.
Start with 1 piece. After cut 1 there are 2 pieces, after cut 2 there are 3, after cut 3 there are 4, and after cut 4 there are 5. So 5 pieces need 5 − 1 = 4 cuts.
Each cut takes 2 minutes, and the cuts happen one after another with no stacking, so the time is 4 × 2 = 8 minutes.
The usual wrong answer is 10 minutes, from multiplying 5 pieces by 2 minutes. That counts one cut too many: the last piece is simply what is left over after the fourth cut, and it never needs its own cut.
This is the same off-by-one idea as fence posts and gaps: pieces are one more than cuts, just as posts are one more than gaps in a straight fence. Quick check with a small case: 2 pieces need 1 cut, which takes 2 minutes, not 4.
Learn the method: Fence Post Riddle: Why a 15 m Fence Needs 6 Posts
