MATHS WEEK MAY coming to an end, but don’t worry, we still have one more set of puzzles for you.

Scare-rithmatic

Hopefully you had fun celebrating Maths Week with the Journal. It is estimated that over a half a million people across the island participated in Maths Week this year, in schools, at partner centres and in large-scale events such as Maths in the City Dublin, Belfast, Cork and Limerick and Celebration of Mind at the Botanic Gardens. Below is a final set of challenges with a Hallowe’en theme to see out the week.

1 Áine, Briain and Ciara come home on Hallowe’en night with a bag of sweets they collected and set about dividing them up. Áine was the eldest and claimed she should have half the sweets. Briain declared that since he was next eldest, he should take half of what’s left. Ciara was upset to see that her share was only 6 sweets. How many sweets were there all together?

2 Everyone on the WhatsApp group was invited to the Hallowe’en party. A message followed directly. “Bring a pumpkin for everyone (including yourself) at the party to do pumpkin carving.” This second message was not meant for everyone, but everyone complied and turned up with the requested pumpkins. There were 25 pumpkins in all. How many in the group?

The children went collecting from a terrace of four houses. They came home with apples, oranges, sweets and monkey nuts. When their parents asked from whom they got the different items, they answered all at once. The best the parents could make out was the following statements.

We got the apples two doors to the left of Mr Brown and the monkey nuts to the
right of Mr Brown

Ms White did not have fruit

Ms White lives next door to Mrs Black

We did not get the apples and oranges from two adjacent houses.

Ms Gray did not give apples or sweets

Can you work out where the children got what?

4. On the eve of All Hallows, I saw the witch’s coven flying in single file. I saw a witch in front of two witches, a witch between two witches and a witch behind two witches.
How many witches was there all together?

5. The children came back from their trick and treating with a bag of coins. There was a
mix of 20c and 50c coins and when they finished counting, they found there was 16
coins and the total value was €5.00. How many 20c pieces and how many 50c pieces were there?

6. I have a basket of sweets to give out at Hallowe’en. There isn’t more than 100 and I
want to divide them into even packs. I find if I divide them by 5, I get a remainder of
4; if I divide by 4, I get a remainder of 3; if I divide by 3, I get a remainder of 2 and if
I divide by 2, I get a remainder of 1. How many sweets do I have?

7. There are 8 people at the Hallowe’en party. Can you figure how to cut the barmbrack into 8 equal portions using just 3 straight cuts?

8. Wanting to have a traditional Hallowe’en party, you order three boxes of apples, a
box of green apples, a box of red apples and a box of mixed green and red. The
delivery person tells you that all of the boxes have been mislabelled, but they will open one a little way (without being able to see into the box) and take out one apple and will be able to tell you the correct labelling. Can you figure out how they could do this?

Saturday’s puzzles: The answers

Hero’s great insight was to imagine the starting point (Jack’s House) reflected across the river as a point an equal distance from (Jack’s side of) the river.

The shortest distance from this new point to Jill’s house is in s straight line. The point at which this line crosses the river, marks the shortest path from Jack’s house to the river and onto Jill’s house.

Eoin Gill Eoin Gill

Come back tomorrow for the answers to today’s puzzle. 

The puzzles this week have been compiled for The Journal by Eoin Gill of Maths Week Ireland and South-East Technological University (SETU).