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Bridge · two-digit B11 factor
B11 Soft
A two-digit factor is coded as 11a + b. One starting product, one Killer Move, and one added product lead to the answer.
Keep the larger factor as the base. Encode the two-digit smaller factor as 11a + b, where b is from 0 to 10. The anchor is the largest multiple of 11 not exceeding that factor. Its quotient gives a; its remainder gives b. Each code symbol is a base-eleven digit; X means ten, not multiplication. 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: 47 × 28 — build code 26
- The smaller factor is 28. The anchor is 22 = 2 × 11, because the next multiple, 33, is too large.
- Remainder: 28 − 22 = 6. So a = 2, b = 6, and the code is 26. Decode it: 2 × 11 + 6 = 28; it does not mean decimal 26.
Apply the code — one ×11 step
- Start: 47 × 2 = 94.
- Multiply the start by 11: 94 × 11 = 940 + 94 = 1 034.
- Extra product: 47 × 6 = 282.
- Add: 1 034 + 282 = 1 316. This equals 47 × (2 × 11 + 6) = 47 × 28.
Zero and X
- 10 = 0 × 11 + 10 → code 0X. Keep the zero. 21 = 1 × 11 + 10 → code 1X.
- For 47 × 21: start 47; ×11 gives 517; add 47 × 10 = 470; total 987.
Use “Apply code” to learn the ladder with a supplied code; “Build code” to practise anchor, remainder and code; “Do everything” combines both. In the ladder, add base × b, not just b. The three levels keep this rule and increase the size of the base.