The post Deputy First Minister’s Holiday Maths Challenge – Spring 2020 solutions appeared first on Making Maths Count.

]]>Deputy First Minister’s Spring Maths Challenge Solutions

The post Deputy First Minister’s Holiday Maths Challenge – Spring 2020 solutions appeared first on Making Maths Count.

]]>The post Give your views on the Deputy First Minister’s Holiday Maths Challenge appeared first on Making Maths Count.

]]>This online survey will only take a few minutes to compete and will help to shape what the Challenge might look like in the future: bit.ly/2SXvbNR

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]]>The post Deputy First Minister’s Christmas Maths Challenge 2019 appeared first on Making Maths Count.

]]>DFM’s Christmas Maths Challenge 2019 – Solutions

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]]>The post Maths Week Scotland 2019 – Mixed Doubles appeared first on Making Maths Count.

]]>**Problem 7: Mixed Doubles**

Eight keen tennis players played a mini mixed-doubles tournament one Saturday afternoon and then went on to a dance in the evening. They are Andy, Clarissa, Emma, Gordon, Jan, Liz, Sunita and Zak. At one point during the evening:

- Emma was dancing with Zak
- Liz was dancing with Clarissa’s tennis partner
- Sunita was dancing with Liz’s tennis partner
- Andy was dancing with Gordon’s tennis partner
- Gordon was dancing with Zak’s tennis partner

Identify the pairs of tennis partners.

**Solutions to Problem 7:**

**Answer** The pairs of doubles partners were:

Zak and Sunita, Gordon and Liz, Andy and Clarissa, Jan and Emma.

Since Emma was dancing with Zak, by the next two statements, Zak cannot be Clarissa’s tennis partner (as Liz was dancing with him) and also cannot be Liz’s partner (as Sunita was dancing with him). Zak cannot be Emma’s partner, since by the last statement Gordon was dancing with Zak’s partner. So Zak was partnered by Sunita.

As Gordon was dancing with Sunita, by the third statement, Gordon was Liz’s partner.

So Andy was dancing with Liz and by the second statement Andy and Clarissa were partners.

That means that the final doubles partnership was Jan and Emma.

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]]>The post Maths Week Scotland 2019 – Stripes appeared first on Making Maths Count.

]]>**Problem 6: Stripes**

In Wuppertal Zoo, there is a tank containing 41 spectacular tiger fish. Each male fish has 111 stripes while each female has only 37 stripes. Unfortunately, the male fish caught a disease and two thirds of them died. How many stripes were on display in the tank after this?

**Solutions to Problem 6:**

Answer 1517

Note that 111 is three times 37 so each male fish had three times as many stripes as a female fish. When two thirds of the male fish die, two thirds of the male stripes disappear. This gives the same number of stripes on male fish as we would have **if all the male fish survived** but had lost two thirds of their stripes and so had only 37 stripes instead of 111. So the number of stripes now on display is 41 X 37 = 1517

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]]>The post Maths Week Scotland 2019 – Squares and Rectangles appeared first on Making Maths Count.

]]>**Problem 5: Squares and Rectangles**

a) In the design below, how many squares (of all sizes) are there?

a) How many rectangles are there? (Remember that all squares are rectangles.)

**Solutions to Problem 5:**

The post Maths Week Scotland 2019 – Squares and Rectangles appeared first on Making Maths Count.

]]>The post Maths Week Scotland 2019 – The Extension appeared first on Making Maths Count.

]]>**Problem 4: The Extension**

A contractor was planning a small extension to a house and subcontracting the work to six tradespeople. For some peculiar reason, she worked out what she would have to pay in total to certain pairs of them, as follows:

a) £18000 to the builder and the joiner

b) £9000 to the joiner and the roofer

c) £3800 to the roofer and the plasterer

d) £1500 to the plasterer and the electrician

e) £1200 to the electrician and the plumber

f) £6500 to the plumber and the joiner.

How much did she pay to each tradesperson individually and what was her total outlay?

**Solutions to Problem 4:**

From b) and c), the joiner gets £5200 more than the plasterer.

From d) and e), the plasterer gets £300 more than the plumber.

So the joiner gets £5500 more than the plumber.

But from f), the joiner and the plumber get £6500 between them.

So the joiner gets £6000 and the plumber gets £500.

From e), the electrician gets £700.

From d), the plasterer gets £800.

From c), the roofer gets £3000.

From a), the builder gets £12000.

The total outlay is the sum of the payments to the six, i.e. £23000.

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]]>The post Maths Week Scotland 2019 – Sums appeared first on Making Maths Count.

]]>**Puzzle 3: Sums (almost) without Adding**

If the first ten positive whole numbers are added, the sum is 55. Check it for yourself!

Use this information to find quick ways to sum the:

a) whole numbers from 11 to 20

b) first ten even numbers

c) first ten odd numbers

d) first twenty whole numbers

e) first twenty multiples of 3

**Solutions to Puzzle 3:**

Answers a) 155 b) 110 c) 100 d) 210 e) 630

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]]>The post Maths Week Scotland 2019 – The Test appeared first on Making Maths Count.

]]>**Problem 2: The Test**

a) In 2018, a 26-question test was given to some survey volunteers. Questions that were answered correctly received 8 points, while those answered incorrectly were given a 5-point penalty. If Dipak tackled all the questions and scored zero overall, how many questions did he get correct?

b) For the 2019 test, the same questions were used again but with four new questions added. The scoring system was the same as for 2018. All the volunteers tackled all of the questions but none of them scored zero. Explain why this was bound to happen.

**Solutions to Problem 2:**

Answers a) 10 b) n/a

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]]>The post Maths Week Scotland 2019 – Broken Calculator appeared first on Making Maths Count.

]]>**Problem 1: Broken Calculator**

Doing calculations on an old and broken basic calculator is very tricky. The problem with this calculator is that it has only five (white) buttons still working. They are the 3 and the 9, the buttons for adding and dividing and the equals button. (The red buttons don’t work at all.)

Danny has done a calculation that led to the answer 40. We know that he made no more than eight button presses. Find three sequences of buttons that he could have pressed.

**Solutions to Problem 1:**

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