Rod Measures

Using 3 rods of lengths from 1 to 10 units, and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units.

For example with rods of lengths 3, 4, and 9 the measurements are:

4 – 3 = 1;   9 – 4 – 3 = 2;   3;   4;   9 – 4 = 5;   9 – 3 = 6;   3 + 4 = 7;   9 + 3 – 4 = 8;   9 and 9 + 4 – 3 = 10 (as illustrated).

How many ways can you find to do all these measurements with 3 rods?

Using 3 rods of ANY integer lengths, what is the greatest length N for which you can measure all lengths from 1 to N units inclusive? Can you beat 10 units?

What is the greatest length that can be measured using 4 of the rods in this way?

Click here to download the ROD MEASURES worksheet.

Click here to download the ROD MEASURES Guide for Home Learning

Click here for Notes for Teachers.

This problem is adapted from the NRICH task of the same name with permission of the University of Cambridge. All rights reserved.