Tonight,
thinking is the key.
A good solution starts with a good question. Observe, eliminate, change strategy and find an explanation that holds up.
Choose a challenge ↓Browse pastimes ↗The library keeps its secrets.
Four unmarked vessels sit on the desk. An incomplete board lies by the fireplace. Twelve identical coins wait beneath the balance. Each object poses a real mathematical problem: choose a case and work through it at your own pace.
Four unmarked vessels
Split nine litres into three equal quantities without estimating.
NRICH · Pouring the Punch Drink✓ 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✓ SolvedThese are adaptations of classical problems published by NRICH and MIT OpenCourseWare. The setting is original; each case shows its mathematical rules and sources. All three challenges remain available year-round.
Browse intermediate challenges too ↗One person proposes. Another tests.
Before opening a hint, explain what you tried and ruled out. A good question may help more than an answer. No timer or automatic sounds.