AS IS OUR annual tradition for MATHS WEEK, we’ve been setting our readers daily puzzles. As we enter the final couple of days, give them a go! 

Maths is too often seen as something that exists only in school textbooks when in fact
there’s a whole world of wonder waiting to be shared with everyone.

The great American recreational mathematics writer Martin Gardner died on 21 October 
2014 at the age of 95. With more than 100 books to his name and 25 years of his column
“Mathematical Games” in the Scientific American magazine, he was a major influence on
recreational mathematics.

Apart from inspiring multitudes of young people in maths and other STEM subjects he also provided a means for the general public to engage with maths.

This is also what our Maths Week puzzles aim to do.

In a material world where appearance is often valued over substance, Gardner celebrated
the mind. At or around the anniversary of his death people commemorate Gardner’s legacy and celebrate recreational maths.

Our “Celebration of Mind” takes place tomorrow at the Botanic Gardens in Dublin, where we will have puzzles, games and shows for everyone. Come along if you can. We’d be delighted to see you.

And now for today’s questions…

Visual spatial thinking is a vital part of learning, problem solving and creativity. Puzzles are a great way to develop these skills. Today we present a selection of challenges that, for a change, don’t involve numbers or other mathematical tools.

1. Is one of these shapes longer than the other. If so, which?

2. Look at this shape: 

Which of the following is the mirror image of it?

3. Which of the following shapes will not fold into a cube?

4. Look at this cube: 

Which of the coloured nets below could fold into this cube?

5. What colour will be opposite green on the cube above? 

***

The answers: Friday’s puzzle 

1. 5 days

They will dig 15 + 20 + 25 = 60 metres in a day.

It is 300m long.

300/60 = 5 days

2. 2 days

Let’s call the workers A, B & C and note that all the walls are equal length which we will call W.

A can build a wall in 4 days, so his rate is W/4 or a quarter of a wall in a day.

B can build in 6 days so his rate is W/6 (1/6 wall in a day).

C can build in 12 days so his rate is W/12 (1/12 wall in a day).

Adding these rates together we need to use 12 as a common denominator:

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(3W + 2W + W)/12 is overall rate = 6W/12 = W/2

This is half a wall per day, so it would take 2 days. 

3. 40 minutes

Let’s call the rate at which the animals eat: Cow, C; Goat, G; Turkey, T; and call the Bag, B.

C + G = B/45

C + T = B/60

G + T = B/90 

Adding these all together we get:

2C + 2G = 2T = B/45 + B/60 + B/90 

We need to express each fraction with a common denominator to add them: 

2(C + G + T) = 4B/180 + 3B/180 + 2B/180

2(C + G + T) = (4B + 3B + 2B)/180 = 9B/180 = B/20

2(C + G + T) = B/20

(C + G + T) = B/40

Therefore, the three animals together eat the bag at a rate of a bag in 40 minutes. 

Come back tomorrow at 7.30pm for the answers to today’s questions and a brand new challenge.  

These puzzles were prepared exclusively for The Journal by Eoin Gill, co-founder and co-ordinator of Maths Week Ireland.