# Maths Puzzles

It’s an extremely difficult time at the moment with COVID-19 and as of 24th March, lockdown in the UK. Most children and parents are at home for the foreseeable future. Keeping everyone occupied is not easy. So we wanted to do our bit to help by adding a “Puzzle a Day” until the lockdown is lifted. Just to keep the mind occupied and ticking over! During the coming weeks, we will be adding a series of different puzzles that are hopefully seen to be challenging. **Parents can also participate in this and make it a fun family exercise.**

#### Question

**TASK: **

**QUESTION: ****See above….How many moves will it take to get all the coins on heads?**

**Time allowed: 20 mins**

#### Answer

#### Question

**TASK: **

When asked about her birthday, Menka said:

“The day before yesterday I was only 25 and next year I will turn 28.”

**QUESTION: ****This is true only one day in a year – when was she born?**

**Time allowed: 10 mins**

#### Answer

A bit of logical thinking is required….

**The lovely Menka was born on December 31st and spoke about it on January 1st.**

`The day before yesterday I was only 25…’

Dec 30: 25

Dec 31: 26

Jan 1 (this year): 26

‘…next year I will turn 28’

Dec 31 (this year): 27

Dec 31 (next year): 28

#### Question

**TASK: **

The number 8549176320.

**QUESTION: ***What is unique about the above number?*

**Time allowed: 10 mins**

#### Answer

**It represents the digits 0 to 9 in alphabetical order:**

8 Eight

5 Five

4 Four

9 Nine

1 One

7 Seven

6 Six

3 Three

2 Two

0 Zero

#### Question

**TASK: **

With you, you have 3 bags of marbles. Within each bag are 2 marbles.

**Bag 1** – 2 Black Marbles ; **Bag 2** – 2 White Marbles; **Bag 3** = 1 White and 1 Black Marble

You pick a bag completely at random and take out a marble at random. It is a white marble

**QUESTION: ***What is the probability that the remaining marble from that bag is also white?*

**Time allowed: 10 mins**

#### Answer

**So lets go through this step by step:**

- Because you have 1 White marble, you know you do not have the Bag 1 which has 2 Black Marbles. Therefore, there are 3 possibilities:
- You choose
**Bag 2**. The first white marble you have. The second marble is also white - You choose
**Bag 3**. The first white marble you have. The second marble is black

- You choose
- So, 2 out of 3 possibilities are white. Answer
**2/3**

#### Question

**TASK: **

A murderer has been condemned to death. He has to choose between three different rooms. The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven’t eaten in 3 years.

**QUESTION: ***Which room is safest for him?*

**Time allowed: 10 mins**

#### Answer

**This is an easier one**

It has to be the **3rd room** because the lions have not eaten in 3 years. Therefore, they must be dead

#### Question

**TASK: **

There were 2 workers’ coming back from work one evening. (Worker A and Worker B). They hired a taxi to take them home from the office.

Worker A lived 15km away from the office and Worker B lived 30km away from the office. The road to Worker Bs home went directly past that of Worker A.

In total, the trip cost £40.

**QUESTION: ***What would be a fair allocation for each worker to pay of the total £40 trip?*

**Time allowed: 20 mins**

#### Answer

**So lets go step by step:**

- For the first 15km, Worker A & Worker B share equally £20 of the total £40 bill (as its half way of the journey);
- This would therefore be £10 each that they pay up to that point
- Then Worker B continues home for the remaining 15km of the journey
- The cost of this remaining part of the journey would be £20
- Therefore,
**Worker A pays £10 and Worker B pays £30**

#### Question

**TASK: **

After visiting Uncle Sam, I started the long journey back home in his truck. The truck was quite dated and old and it also had a bit of a leak from the petrol tank, and I would not move out of third gear.

As a result of this, all I could do is travel at a constant 40 miles per hour. Also all I could get was a mere 20 miles per gallon of fuel.

What I did before I left was to place precisely 15 gallons of fuel into the fuel tank. There was one issue though which is that the fuel tank lost fuel at the rate of half a gallon per hour.

The moment I arrived home, the truck stopped as it had run out of fuel

**QUESTION: ***What was the distance from Uncle Sams house to my home?*

**Time allowed: 20 mins**

#### Answer

**Quite a tricky question so the best way to deal with this is to break it down step by step:**

1. I was travelling at 40 miles per hour at a rate of 20 miles per gallon.

2. Therefore, I was using 2 gallons for every hour whilst driving (40mph/20mpg)

3. 0.5 gallons was being lost per hour so really, I was using 2.5 gallons per hour

4. Therefore, to use up the 15 gallons of fuel, I was travelling for 6 hours (15 gallons/6 hours)

5. 6 hours at a rate of 40 miles per hour means I was driving for **240 miles**

#### Question

**TASK: So the challenge for today. Using the numbers 1, 3, 5, 7, the multiplication sign, the addition sign and equals sign, what is the largest number you can make? **

**RULES: **

1. You are allowed to use each digit and each sign once only.

2. You have to use all of the digits. However, you do not have to use all of the signs

**Time allowed: 20 mins**

#### Answer

**Normally, people come up with 3 possible options. Let’s grade these Good, Very Good and Excellent!**

**GOOD – **What most people do is 75 x 31. So they come up with is **2325. **If you got this answer, then well done. You graded Good!

**VERY GOOD – **Remember. You do not have to use the signs. So you could have got to a larger number by just putting all of the digits together. This would give you **7531. **If you got this answer, then awesome. Very Good!!

**EXCELLENT – **So whats the excellent answer? Well there is a neat little trick. If you are razor sharp (which we know many of you are!), then you could have got a total of **56,715,961. **How did we get that you ask?? Well its with the use of a calculator. Neat trick as we say. If you type in “7531 x = ” into a calculator, then it effectively performs the function 7531 x 7531. So 7531². When you do this, you get the extremely large number of 56,715,961. Now, if you got this, then that is absolutely brilliant. In fact its EXCELLENT!!!

#### Question

**Task: Put the numbers 1 – 8 in each of the squares so that each side adds up to the middle number**

**Time allowed: 45 mins**

#### Answer

**Many different ways of solving this question. Please see below for one possible combination:**