Figures for Fun · Brain-teasers for lunch
Seven riddles from a rainy afternoon — each one animated, each one hiding a real idea about words, numbers and the shape of the world.
A walker went four times around a birch in a round glade, but the squirrel on the trunk kept turning its face towards him. Did he circle the squirrel or not?
“Call that circling round the squirrel when I didn’t see its back?”
Concept: Definitions come first — arguments about words are not arguments about facts.
Every column is a day of the quarter. Day 61 is the only column where all five stripes light up at once.
Five clubs meet every 2, 3, 4, 5 and 6 days, all starting on January 1. In the 90-day first quarter (January 1 excluded), how often do all five meet on the same day — and how many days does nobody meet?
Concept: Least common multiples, and counting what is left over with inclusion–exclusion.
X puts in 3 logs, Y puts in 5, and Z contributes 8 kopecks instead of wood. All three share the fire equally. How should the 8 kopecks be split?
Concept: Fair division: you are paid for what you contributed beyond your own share.
Standing at the door
Walking up and down
= same total
One man counted passers-by from his doorway for an hour; the other counted while pacing the pavement. Who counted more?
Concept: Relative motion: the flow of people through a stretch of street is the same for both observers.
Grandson
1816 or 1916
born 1916 → in 1932 aged 16
Grandfather
1866 or 1966
born 1866 → in 1932 aged 66
In 1932 a boy was as old as the last two digits of his birth year — and his grandfather said the very same was true for him. How old was each?
Concept: Setting up an equation: birth year + age = current year, in two different centuries.
Each square is a “from → to” pair. The diagonal (same station) is empty, and A→B is a different ticket from B→A.
25 × 24 = 600
A line has 25 stations, and a separate ticket exists for every section, in each direction. How many kinds of tickets must the station keep?
Concept: Ordered pairs — permutations, not combinations.
500 km east up north spans more longitude than 500 km west back home.
From Leningrad: 500 km north, 500 km east, 500 km south, 500 km west. Where does the helicopter land?
Concept: The Earth is a sphere — a degree of longitude shrinks as you move towards the pole.
Every riddle at that table turned on the same habit of mind: settle what the words mean, then let arithmetic and geometry do the rest. Agree on the definition, and the argument dissolves.