The reasoning collection.
Choose by difficulty or the kind of thinking you want to explore. Hints, fresh perspectives and solutions are available within each problem.
From a good idea
to a proof.
Six problems, three levels. Start at intermediate or jump into a bigger challenge.
Nine coins, two weighings
Find an anomaly by designing comparisons that eliminate possibilities.
NRICH · Find the Fake✓ SolvedBridge and torch
Crossing is only the start: find a strategy with the minimum total time.
NRICH · Crossing the Bridge✓ SolvedFour unmarked vessels
Split nine litres into three equal quantities without estimating.
NRICH · Pouring the Punch Drink✓ SolvedThe hundred-door corridor
A hundred passes change the locks. Find a rule that avoids simulating every pass.
Plus · Jail break✓ SolvedThe board with two missing corners
Searching more arrangements may not help. Decide whether a solution exists and prove it.
MIT OpenCourseWare · Mathematics for Computer Science, problem set 5✓ SolvedTwelve coins, unknown weight
One coin may be heavier or lighter. Design three weighings to identify both facts.
NRICH · Find the Fake✓ SolvedA problem worth returning to.
Each day we highlight one of the six collection problems. Explore the others whenever you like. The selection changes at midnight UTC.