Number Rods
Saved ways are kept for each pair.
Can you make every number from 1 to 20 using only 3-rods and 4-rods? Use as many as you like. Add to move right, or subtract to move left.
Start at zero. Choose a rod below.
My ways to make 1
0 waysReach the target, then save your discovery here.
Investigation ideas & help
Try a target in any order. You can go past it and come back, or travel below zero. Each coloured bar is one rod, drawn to its number length. Choose one odd rod and one even rod at the top. Some pairs can make every target; others cannot.
- Can you reach every target using addition only? Which ones need subtraction?
- Can your chosen pair make 1? What does that tell you about the other targets?
- Can you find another way using fewer rods?
- What happens if you change the order of your moves?
With rods 3 and 4: 4 + 4 + 3 = 11, and 4 + 4 − 3 − 3 = 2. With rods 3 and 6, every result is a multiple of 3, so some targets are impossible. For any reachable target there are endlessly many ways when you can add and subtract; try finding a few. Different orders are saved as different ways.
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