1.1.7 Logic puzzles and problem solving notes

1. 1.1.7.1Cryptarithms: letter-to-digit sums and products

   In a cryptarithm each letter is a different digit; solve it column by column from the units, using three levers — the carry (never more than 1 when two numbers are added), the leading digit (never 0, and 1 when the sum gains a digit) and unit-digit patterns.

   Advanced · 7 min · Full course
2. 1.1.7.2Weighing, balances and counterfeit-coin puzzles

   A two-pan balance has three outcomes (left down, right down, level), so each weighing can cut the suspects to one-third — which is why powers of 3 run through every counterfeit-coin and weights puzzle.

   Advanced · 7 min · Full course
3. 1.1.7.3River crossing, water jugs and sequencing puzzles

   Puzzles of moves and order are solved by writing the state after every move (who is where, how much is in each jug, what is done) and refusing any state that breaks a rule — the shortest list of safe states is the answer.

   Advanced · 8 min · Full course
4. 1.1.7.4Magic squares, number grids and grid logic

   Grid puzzles give each row, column or line a rule — equal sums in a magic square, each value once in a Latin square or sudoku, one match per person in a logic grid — and are solved by filling the cell with the fewest possibilities first.

   Advanced · 8 min · Full course
5. 1.1.7.5Tournaments, games and strategy: knock-out, round robin and last-move wins

   Tournament questions are counting — every knock-out match removes one player and every pair meets once in a league — while strategy games are won by always handing the opponent a losing position, found by working backwards from the end.

   Advanced · 7 min · Full course

Medha AI is an independent preparation service. It is not affiliated with, endorsed by or connected to APPSC, TSPSC, MPSC, UPSC or any other commission or government body.