# Maths Wizard Challenge

## This Week’s Maths Wizard Problem…

**Hello young Maths Wizards!**

**I hope you enjoyed answering my wizarding conundrums.**

**I will keep posting questions for you each week over the summer and there will be a new Wizard Competition, with leader boards, in September.**

**For more great problem solving questions to keep you Maths Wizards busy during the summer holidays, please also check out my new tab, Further Resources, which includes some fun maths websites for you to try.**

**So click on my wand for this week’s wizarding maths problems**.

**Good Luck!**

**13 July 2020**

**We have two questions for you this week to test your mathematical thinking.**

- Molly cuts a cake into 10 large pieces. She then takes half of these and cuts them into 3 medium pieces each. Finally, she takes a third of the medium pieces and cuts each of them into 2 small pieces.

(i) How many pieces of cake are there at the end?

*For an even trickier challenge try this:*

(ii) Barney takes one piece of each size. What fraction of the original cake does this represent?

*Check back next week to see if your answers are correct!*

**Here are the answers to last week’s conundrums:**

1) The diagram below shows a partially completed magic square in which, all rows, columns and diagonals add up to the same number.

Work out the value of X and y.

*Answer: 13*

2) **Without using a calculator**, work out 123123123123 ÷ 123

*Answe**r: **1001001001*

**Well done if you worked out the right answers!**

1) Eliot buys some sweets which cost 12p each.

He pays for them with three £1 coins.

Maya buys the same number of chocolates which cost 17p each.

She pays for them with four £1 coins.

They each receive the same amount of change.

How many sweets did Eliot buy?

**Answer: 20**

2) The Maths Wizard chooses two numbers from the list below.

987.37, 987.43, 987.47, 987.53, 987.57, 987.63, 987.67

When you round the Maths Wizard’s two numbers to one decimal place they are equal.

When you round the Maths Wizard’s two numbers to three significant figures they are not equal.

Which two numbers did the Maths Wizard choose?

*Answer: 987.57 and 987.63*

3) How many ways are there to arrange the letters of the word *COLOUR*, so that the

two letter *O*’s are *not *next to each other?

**Answer: 240**

4) Bill can mow the lawn in 15 minutes. Ben can mow the lawn in 10 minutes.

How long would it take Bill and Ben to mow the lawn together?

**Answer: 6 minutes**

5) We say a positive integer is *comical *if exactly one of its digits is a 5.

What is the 50^{th} comical number?

**Answer: 259 **

6) Write

as a decimal.

**Answer: 0.6**

7) Leo: “I am thinking of a positive integer.”

Mary: “How many factors does your number have?”

Leo: “Four.”

Mary: “If you triple your number, how many factors will your new number have?”

Leo: “Five.”

What was Leo’s original number?

**Answer: 27**

8) How many squares are there in this diagram?

**Answer: 55**

9) Several square tiles are arranged in a line to make a long thin rectangle.

The ratio of the perimeter of the rectangle to the perimeter of one square tile is 4.

What is the ratio of the area of the rectangle to the area of one square tile?

*Answer: 7*

**10) **What is the smallest positive multiple of 9, *each of whose digits is either 2 or 3*,

with at least one 2 and at least one 3 appearing?

*Answer: 2223*

*(note: the answer could only be made up of the numbers 2 and 3, and unfortunately *

*many of you included the number 4 in your answers!)*

11) The Maths Wizard is thinking of two numbers.

The difference between his two numbers is 5.

The difference between the squares of these two numbers is also 5.

What are the two numbers? Can you use an algebraic method to find them?

*Answer: 3 and -2 (in any order)*

12) The Maths Wizard is on a train carriage with 80 seats travelling to an important

Maths Conference.

On his journey he noticed that all the seats in his carriage were taken and 7 people were standing.

At the next stop, 9 people left the carriage, 28 people entered it and all seats were taken.

How many people now had no seat?

*Answer: 26*

13) Consider the list of numbers 15, * a *, 23 , 27 ,

*, 35. . . where*

**b***is the second number*

**a**in the sequence and * b *is the fifth number.

a) Write down the values of * a *and

**b.**b) Find the 50^{th} term in this sequence

**Answer: (a) a = 19, b = 31 (b) 211**

14) The perimeter of the regular decagon X is 8 times the perimeter of the regular

octagon Y.

Each edge of the regular octagon Y is 10 cm long.

How long is each edge of the regular decagon X?

*Answer: *64 cm (units optional)

15) A spinner has the letters P, Q, R and S on it.

The probability of spinning an S is 0.1.

The probability of spinning a P is 0.6.

The probability of spinning a Q is the same as the probability of spinning an R.

Calculate the probability of spinning an R?

**Answer: 0.15 (or 3/20 or 15%)**

16) The Maths Wizard went on a bike ride leaving his house at 06:15 and arrived back home at 08:48 later that morning.

How many minutes did his journey take?

**Answer: 153 (minutes)**

**Why not take a look at some more tricky problem solving puzzles at the following websites. Just click on the link and it will take you straight there.**

**Junior Maths Challenge**

https://www.ukmt.org.uk/competitions/solo/junior-mathematical-challenge/archive

**Nrich Website / Twitter** (on twitter they post questions)

https://nrich.maths.org/primary

https://twitter.com/nrichmaths

**Times Tables Rockstars** (great fun reinforcing times table skills, for a small subscription of £6 pa)

**You may also like to take a look at Elastic Numbers, written by one of Hampton’s own Maths Teachers, Mr Griller.**

Available from most book shops and also online, *Elastic Numbers* is full of fun and challenging mathematical treats for the serious problem solvers among you!