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
×123456789101112
10102030405060708090100110120
15153045607590105120135150165180
2020406080100120140160180200220240
25255075100125150175200225250275300
30306090120150180210240270300330360
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.

TableAnchorOffsetWorked example (×7)
1110+111×7 = (10×7) + (1×7) = 70 + 7 = 77
1210+212×7 = (10×7) + (2×7) = 70 + 14 = 84
1315213×7 = (15×7) (2×7) = 105 14 = 91
1415114×7 = (15×7) (1×7) = 105 7 = 98
1515+015×7 = (15×7) + (0×7) = 105 + 0 = 105
1615+116×7 = (15×7) + (1×7) = 105 + 7 = 112
1715+217×7 = (15×7) + (2×7) = 105 + 14 = 119
1820218×7 = (20×7) (2×7) = 140 14 = 126
1920119×7 = (20×7) (1×7) = 140 7 = 133
2020+020×7 = (20×7) + (0×7) = 140 + 0 = 140
2120+121×7 = (20×7) + (1×7) = 140 + 7 = 147
2220+222×7 = (20×7) + (2×7) = 140 + 14 = 154
2325223×7 = (25×7) (2×7) = 175 14 = 161
2425124×7 = (25×7) (1×7) = 175 7 = 168
2525+025×7 = (25×7) + (0×7) = 175 + 0 = 175
2625+126×7 = (25×7) + (1×7) = 175 + 7 = 182
2725+227×7 = (25×7) + (2×7) = 175 + 14 = 189
2830228×7 = (30×7) (2×7) = 210 14 = 196
2930129×7 = (30×7) (1×7) = 210 7 = 203
3030+030×7 = (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