Good Problems

The king of Lydia is planning to attack Persia, and wants to know if the war will be successful. So he goes to ask the nearest oracle. The ...

A long time ago, Bengt was in school, and his teacher taught him some nifty tricks for checking divisibility. Checking if something is div...

Bengt is planning to build a... patio, I guess? Anyway, he's designing a pattern made of little square stones in a square grid. Some of...

Bengt is working on a little nuclear thing in his basement, and it's making him a bit paranoid. He's sure that shady government agen...

Bengt has gone to see a film at the small local cinema. This particular cinema doesn't have seat reservations, so you go inside and pick...

Bengt's friends are playing board games. Bengt, however, is not. He got distracted, as he often does, by trying to improve on what he pe...

In some ways, Bengt is an old-fashioned fellow, and he has thus far kept all his "information", as he says, in little notebooks. L...

The Travelling Salesman is a classic problem. Given n cities, and for each pair of them the time it takes to travel from one to the other, f...

Fermat had a lot of clever ideas in mathematics, but the Fermat primes were maybe not his brightest one. He claimed that any number on the f...

ISO 216 is a lovely standard. It's the one that defines the A4 paper size, and all its friends. Bengt likes papers, not just for writing...

Bengt is in the bath. It's very hot, because Bengt thinks real men bathe in at least 50°C, but that has nothing to do with the problem. ...

In the last problem, we took arithmetic down to what seems like a very fundamental level, seemingly without any preconceived ideas or assump...

Bengt likes maths, and he likes starting from the very basics. So that's what we're doing today. The foundations of arithmetic are ...

Bengt has started a new construction project in his garage. He's been working for weeks, when Alban comes by to see the finished product...

Bengt has no children of his own, for various reasons. Mainly because he's such a big baby himself, most likely. He does occasionally en...

Bengt and Alban are doing some calculations. Actually, Alban is doing some sort of homework, and Bengt is playing around with his calculator...

Bengt is building a machine. It is a most unusual kind of hole puncher. It consists of a holder for the papers, and a rather nasty-looking w...

Bengt's friend Alban is an engineering student, and he's trying to show Bengt that he's not completely ignorant in the more theo...

Bengt is cruising around in his car, when suddenly he comes to a red light. The annoys him very much. In order to minimise his annoyance, he...

Bengt is in the mood for designing a game. But his imagination is not at its best. He was up late last night, and... well, never mind that. ...

Bengt is back from his winter holiday, and he's exhausted. So he sits down by the fireplace with a nice cup of tea. The cup is cylindric...

Bengt and Alban are playing Rock-Paper-Scissors. Unsurprisingly, it soon turns into a discussion of game theory. "Suppose you get one p...

Alban is trying to convince Bengt to play a table-top role-playing game, one of those things with lots of little warlike figurines. "Th...

Bengt is watching "QI" on BBC. It's the kind of show which really gets Bengt going, because he doesn't want to accept that...

It's time for another of the fabled Theme Months, and this month, despite lack of better judgement, Bengt has decided to do something tr...

The aliens flying above Bengt's house are having some difficulties contacting their home planet. They want a unified protocol for sendin...

Bengt is doing his exercise routine. It takes quite a while, mostly because he is too lazy to work very hard, so he doesn't get tired ve...

Sture has finally got tired of playing with marbles, but Bengt continues with the fervor of a true scientist. He is still building pyramids,...

When we left them last week, Bengt and Sture were building pyramids out of marbles. Since time in problem-space is independent of time in th...

Bengt so enjoyed having a themed month, that he insists on doing it again. This time it's Marble Month, so he invites Sture over to play...

Bengt is walking along an infinite straight road. He has 1000 s left to walk. But he also needs to cross the road. The safest way to cross i...

Bengt is feeling ill, and is lying in his bed playing around with ternary logic, modal logic, and some other things that he's not sure a...

Chess Month continues with another very chaotic chess challenge. What should white do? Bengt has come up with another peculiar game. It'...

Bengt doesn't often play chess. It's not that he doesn't like it, but he gets upset when he loses, and people don't like Ben...

There are many kinds of good problems, not just ones involving complicated maths and physics calculations. So, this month, it's Chess Mo...

Bengt and Sture are cruising down the motorway. Bengt is driving. "Why are you driving so slowly?" says Sture. "I'm not d...

Bengt has made a new invention. It's a randomiser. It has a number of wheels, wheels which are partially conductive. The wheels spin, an...

Bengt has come up with a whole new kind of number system, which he has decided to call "Dendriux". Each number is expressed as a f...

Alban is visiting Bengt, and after some drinking they start getting childish and decide to play tag. Bengt is surprisingly fast for his size...

Bengt is having a birthday party and wants to offer his guests something really special. He discusses with Sture what kind of drink you coul...

Bengt and Sture are in the pub. They are drinking beer, obviously, and also playing darts. Bengt has invented a new kind of darts game. It i...

Bengt has a long strip of paper. He puts it on the table, and folds it in half. He lifts up the right hand end, folds it over and puts it on...

It's New Year's Eve, and Bengt is setting up the fireworks. Usually he's not much for safety regulations, but this day he has al...

It's Christmas Eve, and Bengt is celebrating by dancing around a new equation. It looks like this: √(x²+y²)=5-z+f(z)-√(5z) where f the f...

Above Bengt's house floats a spaceship. It's big and round - basically what you would call a "flying saucer". It is held u...

On his desk, Bengt has two cubes. The small cube has the side 2 dm, and the big cube has the side 1 dm. The reason why the 1 dm cube is ...

Bengt has found a number sequence. It starts like this: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, ...

Bengt's friend Alban has started studying at LTH, the Faculty of Engineering at Lund University. He therefore has a sweater with the log...

Bengt is sitting in his hammock, thinking. The hammock is doing a pendulum motion, but that has nothing to do with this problem. "In cl...

Bengt is sitting in the town square eating ice cream. He looks like he is deep in thought. Sture walks by and comes up to him. "Hi ther...

Bengt has a thick metal sheet. It is in the shape of a hexagon with the side 1 m. Now he wants to make it float. Here's his idea: He wil...

Bengt has a big clock on his wall. It's an old mechanical clock, powered by a spring. The spring keeps a pendulum wheel in motion. The p...

"The real numbers are not a countable set." says Alban. "Oh really?" says Bengt, in a somewhat disdainful tone. "Re...