Number riddles

12-step ladder

It is one of those problems that invites us to list paths one by one. There is a much more elegant way to solve it.

Chess and the grain of rice

There is an old legend about the inventor of chess and a king who offered him any reward. The inventor asked for something seemingly simple: grains of rice, doubling…

Cruise Control

Sometimes, increasing something by 10% and then decreasing it by 10% does not take you back to where you started. This riddle comes from one of our readers, who…

Five boxes, ten weighings

Ten results, no labels, and five weights to reconstruct.

Four Marks

Four marks produce exactly six distances. Can you place them so that no measurement is repeated or wasted?

Hilbert I's Hotel

There are few problems so brief and so revealing. Here infinity is not presented as something enormous, but as something strangely flexible: moving everyone still…

SEND MORE MONEY

It is probably the most famous alphametic in mathematical recreation: a verbal sum that looks like a toy and ends up functioning as a chain deduction.

Sum and product

It's a conversation that builds slowly, as only good logical problems do. Each sentence does not provide new information: it erases possibilities.

Synchronized sources

The clue is not always in what moves. Sometimes it is in what remains calm. In this square, a coin falls into the water at a precise moment — and that moment has a…

The "look and say" sequence

It has the appeal of patterns that seem almost visible and yet slip away for a moment longer. There is no hidden algebra: the key is in how each term is observed.

The code with checksum and reverse

A four digit code leaves three traces: a sum, a multiple, and what happens when you read it backwards. Three conditions for a single number.

Curious

The consecutive numbers

There are properties that hold for any possible choice, without exception. This riddle invites you to find why a certain outcome is inevitable, whatever the starting…

The Conway Bus

Two mathematicians, a visible route number, and a single denial that reveals one passenger's age.

The Divided Loot

Every split produces a different number and opens new possibilities. The total seems to depend on the chosen path—until you discover what each product is really counting.

The Hidden Sum

Many numbers can be broken into a staircase of consecutive positive integers. The challenge is to identify the one family that never allows such a decomposition.

The Impossible Stamps

Some numbers look impossible only because we are still too low. With two suitable stamp values, there comes a point after which impossibility disappears forever.

The Incompatible Clubs

How many different groups can coexist under rules that seem almost harmless? Parity conceals a surprisingly rigid limit.

The invisible submarine

It seems impossible to hit an invisible target that could have started at any integer position and moved at any integer speed. However, the impossibility has a crack.

The Last Bucket Full

A problem of transfers and invariants disguised as buckets and marbles: the move looks local, but the decisive idea is global.

The merchant's weights

It has the feel of an ancient problem done right: a merchant, a balance scale, and the need for perfect precision. The beauty here is not in testing combinations one…

The number that describes itself

It seems like a numerical oddity, and it is; but not in the capricious sense. It has that special grace of problems in which each figure imposes conditions on all the…

The Number That Doubles When You Move a Digit

Some numbers seem to have an internal choreography. Move one digit, and instead of becoming scrambled, the number turns into exactly twice itself.

The Number with a Zero Inside

A zero seems to be worth nothing. But placed in the middle of a number, it completely changes the value of its digits. Here the zero does not add: it shifts.

The Remainder Code

A list of remainders can look like a set of unrelated conditions. Sometimes they are all saying the same thing in disguise.

The Square That Ends in Itself

Some numbers leave a signature when multiplied by themselves. They hide at the end of their own square, as if the calculation returned them intact.

The switches and the million light bulbs

A million switches, a million light bulbs, a million passes. The question seems monumental, but it boils down to something much more intimate: the individual history…

The tournament of ties

In a short league, five teams face each other against each other. In the end, neither pair of teams shares a score. The question is how far the fourth placed team can go.

The Two Piles

A game of removing stones can look like a long, boring subtraction. But if you look at what never changes, a hidden measure appears and governs the whole process.

Two Columns

You may split the numbers however you like. Once the two groups are sorted in opposite directions, the final sum no longer depends on your choice.

Water and wine

Two glasses, two transfers and a seemingly very simple question. It is one of those riddles that invite you to calculate right away, although the decisive factor does…

Watermelons in the sun

A percentage changes just one point. The weight, however, does not react with timidity. This riddle is small and leaves a mark.