Arithmetic puzzles | The Guardian

Summer puzzles supplement 2026: the solutions

Guardian Staff — Fri, 31 Jul 2026 23:01:36 GMT

Here are the answers to the puzzles in the Guardian’s 2026 summer puzzles supplement

1. 42.

Can you solve it? The viral maths video that will have you in stitches

Alex Bellos — Mon, 24 Jan 2022 07:10:51 GMT

Are you smarter than Google Assistant?

UPDATE: Read the solution here.

“Hey Google, what’s the factorial of 100?”

There are several clips doing the rounds of what happens when you ask Google Assistant this question. The response is both hilarious and terrifying.

Can you solve it? The count reaches 'twenty, twenty-one'

Alex Bellos — Mon, 28 Dec 2020 07:57:34 GMT

Next year in numbers

UPDATE: For the solutions and further discussion click here.

Count von Count will be fizzing with excitement. For the first time since 1920, the coming year, 2021, consists of two ascending, consecutive numbers. Enjoy this ‘counting date’ while it lasts, people! It ain’t going to happen again for another hundred and one years.

Today’s puzzles reveal more arithmetical patterns concerning 2021.

Can you solve it? Leap year logic

Alex Bellos — Mon, 24 Feb 2020 07:10:14 GMT

Quadrennial questions

UPDATE: Solutions now up here.

It’s not often a leap year comes around. About once every four years, in fact.

To celebrate this year’s bonus day, which falls on Saturday, here are three puzzles about dates and births.

Can you solve it? The poco poco puzzle

Alex Bellos — Mon, 13 Jan 2020 07:10:00 GMT

How to count a little in Spanish

UPDATE: The answer is now available here

How many “fews” do you need until you have “a lot”? In Spanish, the answer to this philosophical conundrum would seem to be 15.

At least, that’s according to the puzzle below, in which the addition of 15 POCOs makes a MUCHO.

Can you solve it? 2020 in numbers

Alex Bellos — Mon, 30 Dec 2019 07:10:00 GMT

The new year deconstructed, and a prize challenge

UPDATE: solutions and results now up

It’s almost the New Year, and – numerically speaking – I’m excited. Not only is twenty-twenty already a bona fide word in the dictionary, but once a month next year there will be a moment in the evening when the time is:

20/20/20/20/2020

Can you solve it? The enduring appeal of Venn diagrams

Alex Bellos — Mon, 29 Jul 2019 06:10:36 GMT

Where pictures and puzzles intersect

UPDATE: Solutions now up here

John Venn – the British logician who around 1880 devised the ‘Venn diagram’ – celebrates his 185th birthday this week.

His idea, a brilliantly simple visual aid to understanding logical relations, is one of the few concepts from abstract mathematics that is easily understood, and regularly used, by non-mathematicians.

Can you solve it? Are you in the smartest 1 per cent (of 13-year-olds)?

Alex Bellos — Mon, 17 Jun 2019 06:10:11 GMT

The test given to the UK’s maths prodigies

UPDATE: The solutions are now up here.

Today you are pitting yourselves against the best 13-year-old mathematicians in the UK.

The questions below are taken from last week’s Junior Mathematical Olympiad, a competition aimed at children up to Year 8 (in England) who score in roughly the top half per cent of mathematical ability.

Did you solve it? Turn it up to 11

Alex Bellos — Mon, 25 Mar 2019 17:00:07 GMT

The solutions to today’s puzzles

Earlier today I set you the following two puzzles:

1) Why is every even digit palindrome divisible by 11? (An even digit palindrome is a palindromic number that contains an even number of digits, like 1221, or 678876.)

Can you solve it? Turn it up to 11

Alex Bellos — Mon, 25 Mar 2019 07:10:01 GMT

A celebration of the number that’s one more than ten

UPDATE: Solution is now posted here

Legs eleven, Ocean’s Eleven, elevenses!

Yes, let’s hear it for the number 11, star protagonist of today’s puzzles.

Can you solve it? 2019 in numbers

Alex Bellos — Mon, 31 Dec 2018 07:30:10 GMT

Calculations to kick-start the new year

UPDATE: To read the solutions click here.

To welcome the New Year, we’re going to celebrate the number 2019. Here’s one numerical factoid readers may find charming:

Thanks Ed! Please add your pleasing 2019 number patterns in the comments below. Meanwhile, today’s puzzles:

0 x (2 + 1 + 9) = 0

2 – 1 + (0 x 9) = 1

Did you solve it? Head-spinning bicycle puzzles

Alex Bellos — Mon, 16 Jul 2018 16:00:41 GMT

The answers to today’s puzzles

In my puzzle blog earlier today I set you the following three challenges:

1) The King of the Mountains went up the col at 15 km an hour and down it at 45 km an hour. It took him two hours in total. Assuming that the distance he travelled up and down are the same, how far is it from the bottom to the top of the col?

speed = distance/time

Can you solve it? Head-spinning bicycle puzzles

Alex Bellos — Mon, 16 Jul 2018 06:10:29 GMT

Run your brain through the gears

UPDATE: Click here for the solutions.

Bonjour guzzleurs,

As we are almost midway through the Tour de France, I thought it would be a good moment for some bicycle puzzles.

Did you solve it? The puzzle with a twist

Alex Bellos — Mon, 23 Apr 2018 16:00:07 GMT

The solutions to today’s puzzles

On my puzzle blog earlier today, I set you the following puzzles:

1) What is numerically interesting about April 25, 1849 - the date of birth of the German mathematician Felix Klein - and why is this year’s anniversary particularly noteworthy?

Did you solve it? Le Sudoku français est arrivé!

Alex Bellos — Mon, 15 Jan 2018 17:00:01 GMT

The solutions (and hints) for today’s puzzles.

In my puzzle blog earlier today, I set you four Garam puzzles.

You can see (and print out) the puzzles by clicking on this link.

Can you solve it? Le Sudoku français est arrivé!

Alex Bellos — Mon, 15 Jan 2018 07:10:49 GMT

Savour a new puzzle from across the Channel

Bonjour guzzleurs!

Today’s puzzle comes from France. It is called Garam, and provides some spice for the brain....

Did you solve it? Try your cluck at these chicken problems

Alex Bellos — Mon, 11 Sep 2017 16:04:42 GMT

The answers to today’s fowl questions

On my puzzle blog earlier today I set these four questions, here restated with the answers:

1. If cocks cost 5 qian each, hens cost 3 qian each and chicks are three for a qian, how many cocks, hens and chicks do I buy if I buy 100 of them altogether for exactly 100 qian.

Can you solve it? Try your cluck at these chicken problems

Alex Bellos — Mon, 11 Sep 2017 06:14:22 GMT

Two thousand years of fowl play has resulted in some truly eggcellent puzzles

UPDATE: The solutions can now be seen here.

Hi guzzlers,

Today I’ve selected four puzzles about chickens, an animal which appears with curious frequency in the history of puzzles.

Did you solve it? Pythagoras's best puzzles

Alex Bellos — Mon, 19 Jun 2017 16:00:40 GMT

The solutions to today’s puzzles

In my blog earlier today I set you the following three problems from Pythagoras Magazine.

1) Dollar bills. In a bag are 26 bills. If you take out 20 bills from the bag at random, you have at least one 1-dollar bill, two 2-dollar bills, and five 5-dollar bills. How much money was in the bag?

Can you solve it? Pythagoras's best puzzles

Alex Bellos — Mon, 19 Jun 2017 06:15:28 GMT

Three teasers from the vaults from the great Greek mathematician and philosopher

UPDATE: The solutions are now up – see them here

Hi guzzlers,

The most famous theorem in maths is named after the Greek thinker Pythagoras. So is the most famous recreational mathematics publication in the Netherlands.