1. Points A, B, C, and D are on the same line. The distance between A and B is 1, the distance between B and C is 2, and the distance between C and D is 4. What can be the distance between A and D? List all possible cases.
2. Points E and F are also on the same line. The distance between D and E is 8, and the distance between E and F is 16. What can be said about the distance between A and F ?

Hints to problem 1.

• Nothing in the problem is said about the order of the points on the line.
• What values can expression 4 o 2 o 1 have if instead of each “o” you put either “+” or “-”? This question has something to do with problem 1.

1. The distance between A and D can be 1, 3, 5, or 7.
2. The distance between A and F can be any odd number of units from 1 to 31.