Reference
Anchor & Adjust cheat sheet
Every number from 11 to 30 sits within 2 of an anchor. Multiply by the anchor first, then adjust.
The five anchor tables
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 15 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 |
| 20 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 | 220 | 240 |
| 25 | 25 | 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 | 300 |
| 30 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 | 330 | 360 |
One route per table
Each table’s anchor, offset, and a worked example multiplying by 7 — generated from the same arithmetic the app uses everywhere else, not typed out by hand.
| Table | Anchor | Offset | Worked example (×7) |
|---|---|---|---|
| 11 | 10 | +1 | 11×7 = (10×7) + (1×7) = 70 + 7 = 77 |
| 12 | 10 | +2 | 12×7 = (10×7) + (2×7) = 70 + 14 = 84 |
| 13 | 15 | −2 | 13×7 = (15×7) − (2×7) = 105 − 14 = 91 |
| 14 | 15 | −1 | 14×7 = (15×7) − (1×7) = 105 − 7 = 98 |
| 15 | 15 | +0 | 15×7 = (15×7) + (0×7) = 105 + 0 = 105 |
| 16 | 15 | +1 | 16×7 = (15×7) + (1×7) = 105 + 7 = 112 |
| 17 | 15 | +2 | 17×7 = (15×7) + (2×7) = 105 + 14 = 119 |
| 18 | 20 | −2 | 18×7 = (20×7) − (2×7) = 140 − 14 = 126 |
| 19 | 20 | −1 | 19×7 = (20×7) − (1×7) = 140 − 7 = 133 |
| 20 | 20 | +0 | 20×7 = (20×7) + (0×7) = 140 + 0 = 140 |
| 21 | 20 | +1 | 21×7 = (20×7) + (1×7) = 140 + 7 = 147 |
| 22 | 20 | +2 | 22×7 = (20×7) + (2×7) = 140 + 14 = 154 |
| 23 | 25 | −2 | 23×7 = (25×7) − (2×7) = 175 − 14 = 161 |
| 24 | 25 | −1 | 24×7 = (25×7) − (1×7) = 175 − 7 = 168 |
| 25 | 25 | +0 | 25×7 = (25×7) + (0×7) = 175 + 0 = 175 |
| 26 | 25 | +1 | 26×7 = (25×7) + (1×7) = 175 + 7 = 182 |
| 27 | 25 | +2 | 27×7 = (25×7) + (2×7) = 175 + 14 = 189 |
| 28 | 30 | −2 | 28×7 = (30×7) − (2×7) = 210 − 14 = 196 |
| 29 | 30 | −1 | 29×7 = (30×7) − (1×7) = 210 − 7 = 203 |
| 30 | 30 | +0 | 30×7 = (30×7) + (0×7) = 210 + 0 = 210 |
Squares, 11² through 30²
11²
121
12²
144
13²
169
14²
196
15²
225
16²
256
17²
289
18²
324
19²
361
20²
400
21²
441
22²
484
23²
529
24²
576
25²
625
26²
676
27²
729
28²
784
29²
841
30²
900
Ends in 5
Take the tens digit, multiply by the next number up, then write 25 on the end. 15²: 1×2=2, so 225. 25²: 2×3=6, so 625.
Step up from the one before
(n+1)² = n² + n + (n+1). So 20² = 19² + 19 + 20 = 361 + 39 = 400.
Glossary