Logic Puzzles & Deduction

Deduction is clue-squeezing: each clue eliminates suspects until one remains. 'Two digits, even, more than 40, digits add to 7.' Start with the SHARPEST clue — digits adding to 7 gives a short list (16, 25, 34, 43, 52, 61, 70…). Now filter: even kills 25, 43, 61; more than 40 kills 16, 34. Survivors: 52 and 70. But 7+0=7 ✓, even ✓, >40 ✓ — two survivors?! Recheck… 70 works too unless another clue splits them. Real tests make clues airtight — and YOU must test every clue against your answer.

Who-owns-what puzzles beg for a grid: people down the side, pets across the top. Read each clue and mark: 'Ana's pet swims' → Ana gets a ✓ under fish — and instantly ✗s fill the rest of her row AND the fish column (one pet each!). 'Ben is allergic to feathers' → ✗ under bird for Ben; with fish gone, Ben must have the cat. Cara inherits the bird. The grid's power: every ✓ triggers a cascade of ✗s.

'Largest possible' puzzles reward a scoring habit. OC flavour: digit cards drawn with straight lines — pick two cards to maximise right angles. Don't eyeball a pair: SCORE each card first (the 4 has 3 right angles, 5 has 4, 6 has 4), THEN pick the top two: 5 and 6 give 8. The same score-then-choose routine wins 'smallest possible', 'closest to 100' and every other optimisation puzzle.

A signature OC format: three statements, and you pick which are correct. OC style: counters 1–15, one taken at random. 'Even and odd equally likely' — COUNT: eight odds (1, 3, 5, 7, 9, 11, 13, 15), seven evens — false! 'More likely above 8 than below 8' — count: seven each (9–15 vs 1–7) — equal, so false. 'A 4 as likely as a 13' — one counter each — true. The method: judge each statement with an actual COUNT, separately, never by gut feel. Then match your verdicts to the answer options.

When a puzzle asks 'how many ways', list like a robot: fix the first choice, run through every second choice in order, then advance the first choice. Two-digit numbers from 2, 5, 7: the 2-family (22, 25, 27), the 5-family, the 7-family — nine, provably. Random listing skips some and repeats others; robot listing does neither. This is also the fallback when magic-shape puzzles resist the clever trick: systematic trial beats scattered guessing. Quiz and exercises now!