Four marks produce exactly six distances. Can you place them so that no measurement is repeated or wasted?
Four Marks
Riddle statement
You have a rod exactly 6 units long.
You must place exactly four marks, including both endpoints.
You want the distances between pairs of marks to be exactly:
1, 2, 3, 4, 5, and 6, each appearing once.
Where would you place the four marks?
Show solution
Solution
Place the marks at:
0, 1, 4, and 6.
The six distances between pairs are:
- 1 − 0 = 1
- 4 − 0 = 4
- 6 − 0 = 6
- 4 − 1 = 3
- 6 − 1 = 5
- 6 − 4 = 2
The six measurements 1, 2, 3, 4, 5, and 6 therefore appear exactly once each.
The placement 0, 2, 5, and 6 is the same solution reflected about the midpoint of the rod.