AS IS OUR annual tradition for MATHS WEEK, we’ve been setting our readers daily puzzles. It’s the final day and we know over 10,000 of you have been taking part. Thank you! 

Sum Hallowe’en Fun

As the sun sets on the 20th Maths Week Ireland, we celebrate an incredible milestone – a cumulative engagement of 5 million people over these years. All thanks to a partnership of universities, schools organisations and people across the whole island. Ní neart go cur le chéile!

The team at The Journal has been a key part of this over the past decade. We thank them for their interest in maths and for enabling us to bring bespoke puzzles and concepts to you, the readers.

From the beginning we have tried to take maths out of the classroom and show how it helps us understand the world around us. Mathematical thinking skills benefit so many parts of our lives. Of course, we also want success in the classroom and research shows that attitude towards a subject is one of the strongest influences on achievement. That’s why we strive to promote a positive attitude towards maths for all.

As we stand on the cusp of the AI revolution, machines are already able to answer most exam-style questions in seconds. But, rather than reducing the need for maths, this new world makes it more vital than ever.

Mathematical thinking – problem-solving, pattern recognition, creativity and reasoning will be the essential human skills in an age of intelligent technology.

We will end the week with a selection of Hallowe’en-themed puzzles.

1. Áine, Brian and Ciara visit their neighbours collecting for their Hallowe’en party. Áine collects 10 sweets, Brian collects twice what Áine collects and Ciara collects twice what Brian collects. How many sweets do they collect all together?

2. I gave half the sweets to the first group of children that called. A quarter to the next group that called and found I had 20 left. How many had I to start with?

3. Xavier collected twice as many sweets as Yvonne for Hallowe’en. Yvonne asked him to share and even things up. Xavier ate two and shared 5 and they then had the same amount. How many did they have to start?

4. Avril, Barry, Ciaran and Darina all collect different amounts of sweets. Avril suggests that they pool their haul and share them out evenly whereby each would get 30 sweets. At that, Barry grabbed his sweets and left. Darina saw that they would each now only get 25 sweets. How many sweets did Barry have?

5. Leprechauns bring their pet spiders out for a walk. Each leprechaun has two spiders and I count 36 legs. How many leprechauns are there?

6. On Hallowe’en, Morrigan leaves Sliabh na Cailleach and flies to the Hill of Uisneach. At exactly the same time Badb leaves the Hill of Uisneach and flies to Sliabh na Cailleach. Morrigan flies at 180kmh while Badb flies at 120kmh. They pass each other after 8 minutes. How far apart are Sliabh na Cailleach and the Hill of Uisneach?

7. The Ban Sí, not being very sociable, didn’t attend the Hallowe’en party but asked the Púca how many people were there.

“All were ghosts, except two. All were leprechauns, except two. All were fairies except two.”

Can you tell the Ban Sí how many were there?

8. Avril, Barry, Ciaran and Darina worked competitively on The Journal puzzles through the week. Eoin asked them how they got on.

Wanting to confuse him, Avril answered first: “Barry was second last and Darina was last.”

Barry chipped in, “Ciaran was actually last and Darina was second.”

Darina added, “Barry was second and Avril was last.”

Exasperated, Eoin turned to Ciaran for help.

“I won’t tell you,” Ciaran announced. “But I will tell you to only believe exactly half of what each of them told you.”

Can you help Eoin work out the ranking?

9. Four children want to divide up the spoils of the Hallowe’en trick or treating. Wanda
insists that as she is the eldest she should decide how to divide up the sweets.

“As I am 12, I will take twelve and a quarter of what’s left.”

“Xavier, as you are 9, you can take 9 and a third of what’s left.”

“Yvonne, as you are 8, you can take 8 and a half of what’s left.”

Related Reads

Maths Week: Your Thursday puzzle

Maths Week: Your Wednesday puzzle

Maths Week: Your Tuesday puzzle

“Wait a minute!” Cried Zelda. “I’m 7 and I would only get 5 sweets.”

How many sweets were there altogether?

10. A group of friends arrange to have a Hallowe’en party. They agree that each person will bring a gift for each of the others. On the night 15 presents were brought and there were 9 presents left over.

How many people were invited to the party (including the host) and how many turned up?

***

The answers: Saturday’s puzzle 

1. They are both the same size.

2. (d) is mirror image.

3. Cannot fold (d) into a cube

4. (c) will fold into the cube

5. Purple will be the opposite face to green. 

Come back tomorrow at 7.30pm for the answers to today’s questions.

These puzzles were prepared exclusively for The Journal by Eoin Gill, co-founder and co-ordinator of Maths Week Ireland. He also gives thanks to Ciarán O’Sullivan.