Problems

Blog posts with problems to get your brain going! You get a new problem every fortnight and the solutions are published later.

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You may notice some problems are missing... I'm still migrating articles from my old blog.

Problem #063 – arbitrarily many primes in arbitrarily big intervals

Can you prove that there are arbitrarily many primes in arbitrarily big intervals?

logic mathematics number theory primes
Problem #062 – sliding coins

Can you align all of the coins on the right edge of the board?

invariant logic mathematics
Problem #061 – flower garden

Three mathematicians discuss a beautiful flower garden and the coloured flowers within.

logic mathematics
Problem #060 – realtor commissions

Two realtors discuss who's netting the award for highest average commission, but it isn't clear who the winner is...

logic mathematics
Problem #059 – marching pegs

How can you swap the coloured pegs if they can only march forward?

logic mathematics
Problem #058 – identifying light bulbs

Please help me identify these 100 light bulbs by turning ON and OFF their switches.

binary logic mathematics
Problem #055 – horse racing

25 horses racing, and you have to find out the fastest ones!

logic mathematics
Problem #053 – weighing the odd one out

Can you find the fake ball by weighing it?

logic mathematics
Problem #048 – trick or treat

Can you help these kids trick or treat their entire neighbourhood in this Halloween special?

combinatorics logic mathematics probability
Problem #047 – surgery gloves

How can two doctors operate two patients with only two pairs of latex gloves?!

logic
Problem #045 – 1, 2, 3

Figure out the number I'm thinking of with a single question!

logic mathematics
Problem #044 – send more money

Can you solve this simple-looking arithmetic challenge?

arithmetic logic mathematics
Problem #043 – Rubik's cube scrambling

If I scramble a Rubik's cube for long enough, will it solve itself?

combinatorics group theory logic mathematics
Problem #042 – mine captcha

Can you solve this little minesweeper puzzle?

game logic mathematics
Problem #041 – canyon crossing

It's night time and 4 friends need to cross a fragile bridge, but they only have one torch. What's the order in which they should cross?

logic mathematics optimisation
Problem #040 – the dozen puzzle

Three friends are given three different numbers that add up to a dozen. Can you figure out everyone's numbers?

combinatorics logic mathematics
Problem #039 – rope timer

You have two magical ropes that you can set on fire and you need to count 45 minutes. How do you do it?

logic mathematics
Problem #034 – one question to happiness

Two doors, one gives you eternal happiness and the other eternal sadness. How can you pick the correct one?

logic mathematics