## This Week’s Maths Wizard Problem…

**Welcome back Maths Wizards! I hope you had a great summer. It’s time to start puzzling again!**

**Click on me for two fiendish puzzles to start our new competition. Good luck and keep wizarding!**

**1 – The Maths Wizard wishes to choose his four-digit padlock code so that it is a multiple of 4 and each digit after the first is one more than the previous digit.**

**What is the code he chooses?**

**2 – We know that 11 ^{2} = 121.**

**Without using a calculator, what is the value of 111 ^{2}?**

If you think you’ve solved this week’s Maths Wizard challenge, fill in your details below together with your answer and we’ll post the solution on Monday 23 September.

Our Maths Wizard problems are aimed at primary school pupils in Year 4 to 6.

**The Maths Wizard buys food for his three puppies in boxes of 24 cans each week. Each of his puppies eats a can of food every day of the week. ****After how many weeks will the Maths Wizard not have to buy any cans for the following week?**

Answer: 7 weeks

**Well done if you answered the question correctly!**

Congratulations to our Summer Term 2018-19 Maths Wizard champions – Isabella from Nelson Primary School, Kavin from St Andrew’s & St Mark’s C of E Junior School and Alex from Buckingham, Browne & Nicols School who all scored 50 points. Well done to our winners and to everyone who took part!

Read all about our Maths Wizard 2018-19 champions here:

maths wizard champions 2018-19

Watch this space for our very first leaderboard of the Autumn Term 2019-20 competition, which will be published on Monday 30 September 2019. Keep wizarding!

**1. The Maths Wizard loves to play games. In one such game you can score either 5, 8 or 12 points each go. What is the highest score that is impossible to achieve?**

Answer: 19

**2. In a training session, Marta takes three strides to cover 10m while Hannah takes four strides to cover 12m. How far apart are Marta and Hannah after they have both taken 300 strides?**

Answer:

Marta: 300/3 = 100

10 x 100 = 1000 metres travelled

Hannah: 300/4 = 75

12 x 75 = 900 metres travelled

Difference = 1000 – 900 = 100 metres

**3. Hannah needs to arrive for a meeting at London Waterloo Station at 0830. It takes her 3 minutes to walk to the bus stop, the bus takes 7 minutes to travel to Windsor and Eton Riverside Station, it then takes her 2 minutes to walk from the bus to the platform, and the train takes 35 minutes to arrive into London Waterloo Station. The buses are unreliable and can run up to 5 minutes late, the trains run on time. Use the bus and train timetable below to work out the latest time she should leave her house to guarantee she is not late for her meeting. **

Answer: Hannah should leave at 0732 and will arrive at exactly 0830.

**4. The Maths Wizard has a square garden with 52 posts positioned every 4 metres around the edge.**

**What is the area of his garden (in square metres)?**

Answer:

52 x 4 = 13

Therefore, there are 13 posts for each side of the square garden

13 x 4 = 52 metres

Therefore, each side of the square garden measure 52 metres

Area = width x length = 52 x 52 = 2704 square metres

**5. Hannah and Daniel each have the same amount of money. **

**If Hannah spends £10 and Daniel £20 then Hannah has three times as much as Daniel.**

**If Hannah spends £15 and Daniel £20 then Hannah has twice as much as Daniel.**

**How much money do they have altogether?**

Answer:

Let a = Hannah’s money and therefore a = Daniel’s money

a – 10 = 3 (a – 20)

a – 10 = 3 a – 60

(add 60 to each side of the equation)

a + 50 = 3a

(subtract a from each side of the equation)

50 = 2a

a = 25

Therefore Hannah and Daniel have £25 each so £50 altogether

**6. Mrs Clarke bought cakes for her class. **

**If everyone in the class had 2 cakes each there would be 10 left over. **

**If everyone had 3 cakes each there would be 15 buns short. **

**How many cakes did Mrs Clarke buy?**

Answer:

Let b = number of pupils in a class

2b + 10 = 3b – 15

(add 15 to each side of the equation)

2b + 25 = 3b

(subtract 2b from each side of the equation)

b = 25

Therefore there are 25 pupils in the class

Cakes = 2 x 25 + 10 = 60

Mrs Clarke bought 60 cakes for her class

**7. If A + Z + Z = 19**

**R + A + M + A = 18**

**T + A + Z = 18 and T = 5**

**where each letter represents a different digit, what is the value of:**

**R + A + Z + Z + A + M + A + T + A + Z + Z**

Answer:

**8. If the following pattern were continued, what would be the sum of the numbers at the start and end of the 10th row?**

** 1**

** 2 3**

** 4 5 6**

**7 8 9 10**

Answer:

**9. Marta’s llamas need a new enclosure. She has 800m of fencing available and can only build using straight line sections. Find:**

**a) the maximum possible area**

**b) the dimensions of the new enclosure**

Answer: A square 200m by 200m enclosure, with area 40,000m²

**10. My famous recipe for apple crumble has only two ingredients: apples and crumble. I need to have 5 parts apple to 3 part crumble for the best possible result. Given that I need to produce a 12kg apple crumble for my guests, how many more kilograms of apples than crumble are required?**

Answer:

12kg = 12,000g

So one part would be 12,000/8 = 1,500g

The difference would be two parts, so 1500 x 2 = 3,000g = 3kg

**11. In a training session, Marta takes three strides to cover 10m while Hannah takes four strides to cover 12m. How far apart are Marta and Hannah after they have both taken 300 strides?**

Answer:

Marta: 300/3 = 100

10 x 100 = 1000 metres travelled

Hannah: 300/4 = 75

12 x 75 = 900 metres travelled

Difference = 1000 – 900 = 100 metres

**12. The Hampton School cheerleading squad is made up of four boys: Tim, Michael, Mark and Daniel, and four girls: Marta, Hannah, Joanna and Caroline.**

**For the cup final, a cheer team of three boys and two girls has to be chosen. However, Mark will not be in the team if Caroline is picked and Marta will not be in the team if Michael is picked.**

**In how many ways could a cheer team be chosen for the cup final?**

Answer: 8

**13.** **A two-digit prime number is added to a two-digit square number and a two-digit cube number. The total of these three numbers is 81. **

**What are the three numbers?**

Answer: 25, 27, 29 (in any order)

**14. The Maths Wizard thinks of a positive number. One less than his number is multiplied by 5 and one more than his number is multiplied by 4. The difference between these two numbers is 1. **

**What is the number the Maths Wizard is thinking of?**

Answer: 10

**15. The Maths Wizard’s country estate covers 8000 m ^{2}. His castle takes up 60% of his estate. A large pond occupies one quarter of what is left and the rest of the estate is footpaths and grass. The area of grass is seven times the area of footpaths.**

**How many square metres of the country estate is covered in grass?**

Answer: 2100 m^{2}

**16. In how many different ways can the word MATHSWIZARD be rearranged to form new 11 letter “words”? (The words do not need to make sense)**

Answer: 19958400

**17. The sum of the numbers from 1 to 100 is 5050. ****What is the sum of all the digits in the numbers from 1 to 100 inclusive?**

Answer: 901

**18. The Maths Wizard buys food for his three puppies in boxes of 24 cans each week. Each of his puppies eats a can of food every day of the week. ****After how many weeks will the Maths Wizard not have to buy any cans for the following week?**

Answer: 7 weeks