When the reasoning needs another step

No. Chords between points on a circle give 1, 2, 4, 8, 16 regions and then 31, not 32. A pattern becomes a rule only when you can explain why it must continue. See the full argument.

Each line sums to 15. The four lines through the centre total 60 and cover all nine cells, with the centre counted four times. So 45 + 3c = 60 and c = 5. Worked example.

Reasoning from the end of a game toward the start. You label each position as winning or losing for the player about to move, then pick moves that hand your opponent losing positions. Try the 21-stone game.

Not directly. Score depends on territory (and, in area scoring, stones on the board). Captures matter when they change territory or the safety of groups.

For a fair coin, no. Each toss is independent, so the chance stays 1/2. Expecting otherwise is the gambler's fallacy.

No. Probability content is educational. No strategy changes the built-in house advantage of commercial games of chance.

The format first appeared as "Number Place" in Dell magazines in the United States from 1979, credited to Howard Garns. The Japanese publisher Nikoli popularised it and named it Sudoku in 1984.

Its documented history begins with Chinese publications in the early nineteenth century. Claims of thousands of years of history are not supported by sources.

Wooden tablets of geometry problems hung in Japanese shrines and temples during the Edo period, often offered by amateurs. Read more.

No. Most worked examples need arithmetic and careful counting. Writing every step down matters more than prior knowledge.