Why the four moves work
Read the card, then follow the algebra once. You do not need to memorise it.
The four moves
For two numbers just below 100:
- Find the deficits — how far each number is below 100.
- Cross-subtract — take one number minus the other number's deficit. That is the left block.
- Multiply the deficits. That is the right block.
- Protect the right block — it always has two digits: 6 becomes 06.
| 98 | 97 | |
|---|---|---|
| Deficit | 2 | 3 |
| Left block | 98 − 3 = 95 | (or 97 − 2 = 95) |
| Right block | 2 × 3 = 6 → 06 | |
| Answer | 95 06 = 9506 |
Why it works
Write each number as 100 minus its deficit, a and b:
(100-a)(100-b) = 10000 - 100a - 100b + ab = 100\,(100-a-b) + ab
- 100 - a - b is the left block. It is the same as (100-a) - b: one number minus the other's deficit. That is why cross-subtracting in either direction gives the same answer.
- ab is the right block. It is added to a multiple of 100, so it fills the last two places — which is why 6 must be written 06.
Check with 98 × 97: a = 2, b = 3, so 100\,(95) + 6 = 9506.
One question to keep in mind
What happens if ab is 100 or more? You will meet that in Section 2.