How to see it
When you know the end and not the start, reverse the steps, in reverse order. Draw the chain, then run it backwards: each step swaps for its opposite. Add becomes take away, times becomes divide.
A worked example
Start at 20. Undo take away 4: add 4, 24. Undo times 3: divide by 3, 8. Check: 8 times 3 is 24, take 4, 20.
The common mistake: applying the operations forwards again
The trap is running the operations forwards again: 20 times 3 take 4. That builds a bigger number from a smaller one. Always reverse. Always check forwards.
Try one
I think of a number, halve it and add 7. I get 15. What was it?
- A8
- B16
- C11
- D44
Show the answerHide the answer
Right: B, 16
15 take 7 is 8, doubled is 16.