MATHS WEEK is coming to a close and, as is our annual tradition, we have set our readers some puzzles every night. Give the last one a go. 

Parting Shot

We have come to the end of the 21st Maths Week Ireland, with over 450,000 people taking part – including you, if you’ve been doing these puzzles!

Thank you for your participation. Remember, as well as being enjoyable recreations, puzzles can help keep your mind sharp and develop your problem-solving skills. So, keep up the good work.

To round off Maths Week, we have some more money sense challenges for you.

1) A coffee costs €4 and a tea costs €3. I bought at least one of each and paid €11. What did I buy?

2) A coffee and two brownies cost €9. Two coffees and one brownie cost €10.50. How much is a coffee?

3) A scone costs €2, a muffin costs €3 and a brownie costs €4. I buy at least one of each, 13 in all. The bill was €30. How many of each item did I buy?

4) Xavier and Yvonne buy 10 doughnuts. Three jam doughnuts cost the same as two chocolate doughnuts. Yvonne says that she will have half the chocolate doughnuts and a third of the jam doughnuts and her contribution will be €10. How much does Xavier owe? 

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Saturday’s puzzle: the answers

1. 90 degrees between the hour and minute hand at 9 o’clock (one quarter of 360⁰)

2. 30 degrees between the hour and minute hand at 11 o’clock (one twelfth of 360⁰)

3. 82.5 degrees between the minute hand and the hour hand at 11.45.

Minute hand is 90⁰ from vertical (12 o’clock).

The hour hand is three quarters of the way from 11 to 12.

The whole clock is 360⁰ so distance between each hour is 360/12 = 30⁰.

The hour hand is one quarter of 30⁰ away from vertical (12 o’clock).

That is 7.5⁰ so angle between minute and hour hand is 90 – 7.5 = 82.5⁰.

4. Clock displays 7pm.

Each real hour, the clock advances 70 minutes.

In 6 real hours (12 – 6pm) it advances 6 x 70 = 420 minutes.

420 minutes is 7 hours, so clock displays 7pm.

5. Correct time will be 5:08:34

The clock advances 70 minutes for every 60 minutes that actually pass.

When the clock displays 6 o’clock, it has advanced 6 hours or 360 minutes on the display. The actual time elapsed is:

(360×60)/70 = 308.57

That is 5 hours, 8 minutes and 34 seconds. 

So, the correct time is: 5:08:34

6. Real time will be 3:17.

The clock runs at a different speed during each hour it displays.

So the clock takes: 60+30+20+15+12=137 minutes or 2 hours 17 minutes

So real time will be 3:17