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Maths Puzzles to Improve Logical Thinking

There are many ways to keep your brain active and improve your logical thinking skills. Some people love to delve into a great work of fiction and immerse themselves in a fantasy world; others are creative enough to produce fascinating works of art. One of my favourite ways to get the cogs turning is with maths and logic puzzles.

These puzzles often start with a seemingly simple question. Once you get into them, you find there’s a lot more to the puzzle than meets the eye. My favourite puzzles are the ones that open up new areas of maths and make you eager to explore them!

Here are some maths and logic puzzles you can try yourself and then use to test your friends and family!

Farmer, Fox, Chicken and Grain

A farmer is trying to get her fox, chicken and grain to market, but first they must cross a river. Fortunately, there’s a small rowing boat she can use. The problem is that the farmer can only take ONE thing in the boat at a time. Also, if the fox is left alone with the chicken, then it will eat the chicken. The same is true if the chicken is left with the grain.
Can you help the farmer get everyone across the river without anything being eaten?

This puzzle was created in the 9th century! Isn’t it amazing to try problems from more than a thousand years ago? Check your answer here.

Cheryl’s Birthday

This problem became famous a few years ago when it was set in the Singapore and Asian School Math Olympiad. It’s actually quite an old question – I remember tackling it in secondary school. The problem goes like this:

Albert and Bernard have just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

• May 15, May 16, May 19
• June 17, June 18
• July 14, July 16
• August 14, August 15, August 17

Then, separately, Cheryl tells Albert the month and Bernard the day of her birthday. The boys had this conversation:

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know either.
Bernard: At first I didn’t know when Cheryl’s birthday is, but now I know.
Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

Read the Wikipedia page on the problem to find out the solution and its steps.

Bridges of Königsberg

Here’s a fun little challenge! There was a town called Königsberg with seven bridges across its canals. They were laid out as shown below. Can you plan a journey that crosses every bridge without crossing any of them twice?

The Maths is Fun site explains the theory behind the problem and gives you a great introduction to graph theory! (Scroll to the bottom if you just want the answer.)