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Method · 3-digit × 3-digit
Full B11
Code the smaller factor as 121a + 11b + c. Then execute the start, two Killer Moves, and two controlled additions.
Full B11 multiplies two three-digit numbers. Keep the larger one as the base and encode the smaller as 121a + 11b + c. Since 121 = 11 × 11, this is also (11a + b) × 11 + c. This explains the two ×11 steps of the ladder. For every ×11 step, use the Killer Move: neighbour sums, then carries. Practise this digit trick on the ×11 page.
How it works — explained step by step
Example: 347 × 256 — build code 213
- The largest multiple of 121 not exceeding 256 is 242 = 2 × 121. Enter anchor 242; remainder 256 − 242 = 14.
- Now split the remainder: 14 = 1 × 11 + 3. Thus a = 2, b = 1, c = 3; code 213.
- Decode: 2 × 121 + 1 × 11 + 3 = 242 + 11 + 3 = 256. The remainder field is 14, not the final digit 3.
Apply the code — the complete ladder
- Start: 347 × 2 = 694.
- First ×11: 694 × 11 = 6 940 + 694 = 7 634.
- First extra product: 347 × 1 = 347. First total: 7 634 + 347 = 7 981.
- Second ×11: 7 981 × 11 = 79 810 + 7 981 = 87 791.
- Second extra product: 347 × 3 = 1 041. Final total: 87 791 + 1 041 = 88 832.
- Check independently: 347 × (250 + 6) = 86 750 + 2 082 = 88 832.
Leading zero and X
- 100 = 0 × 121 + 9 × 11 + 1 → 091. 120 = 0 × 121 + 10 × 11 + 10 → 0XX.
- For 200 × 120: start 0; ×11 gives 0; add 2 000; ×11 gives 22 000; add 2 000; result 24 000.
First practise “Apply code”, then “Build code”, then “Do everything”. The fixed exercise range is three digits × three digits. Every step uses the same base. X is the digit value 10. Always keep all three code positions.