GCSE MATHS SUMMER TASK

“Do not worry about your difficulties in maths, I can assure you that mine are

greater” Albert Einstein

Puzzle 1As a responsible citizen you should always be a little bit wary of what claims adverts make when they want to sell their products. The other day I was listening to the radio and an advertisement came on trying to sell a weight loss pill. It said “If you take this pill once every day for a year you will save 7000 calories”. 7000 sounds a lot and often adverts will use really big numbers to make you think that it’s a ‘good deal’. I was dubious so I worked out how many calories this meant per day.

Approximately how many calories per day are saved if you save 7000 calories per year?

You have a choice of

a) 20b) 40 c) 70d) 100e) 120

This is a problem that was taken from the Senior Maths Challenge. A nice one which anyone could understand but which is also quite tricky.

The letters in the word ANGLE can re re-arranged to make different arrangements, ie GNAEL or LEAGN. There are actually 120 different arrangements for the 5 letters in the word (you get to prove this at A level). If each of the arrangements were put in alphabetical order ie 1) AEGLN, 2) AEGNL... Finishing with 120) NLGEA , where would the arrangement ANGLE appear?

You have a choice of

a) 18th arrangementb) 20th arrangementc) 22nd arrangementd) 24th arrangemente) 26th arrangement

Puzzle 2

Puzzle 3I play five aside football during the week in a five aside league in Norwich. We have a squad of 6 and we are all DIFFERENT heights. Last season we got promoted to the second division (next step Champions League) and we decided to have a team photograph. The photographer (I say photographer, but actually one of the refs) asked us to stand in two rows of three for the photograph according to the following rules:

1) The person on the back row must be taller than the person in front of them2) The person directly on your right, on the same row must be taller than you

How many ways could we all arrange ourselves so we didn’t break the rules?

Extension for mega respect:

What about if there were eight in the team and they had to stand in two rows of four and the same rules apply?

Q: What is the mermaid mathematicians favourite item of clothing?

A: An algae-bra

Who said mathematicians can’t tell jokes hey!?

Mathematics has been studied ever since humans developed language, culture and civilisation. Mathematicians were well respected members of these societies and were in fact the celebrities of the day (not footballers and WAGs like today). These mathematicians would often challenge each other in ‘mathematical duels’. Here is a problem that originally came from those times as a challenge from one mathematician to another.

You have 12 balls identical in size and appearance but 1 is an odd weight (could be either light or heavy).

You have a set of scales (balance) which will give 3 possible readings: Left = Right, Left > Right or Left < Right (ie Left and Right have equal weight, Left is Heavier, or Left is Lighter).

You have only 3 chances to weigh the balls in any combination using the scales.

Determine which ball is the odd one and if it's heavier or lighter than the rest.

How do you do it?

Puzzle 4

Puzzle 5Every 10 years the government issue a census. These are forms that everyone in the country has to complete so that the government has a complete record of everyone living in the UK, what work they do, how many children they have, number of cars etc.

Last time round in the 2001 census I remember my old university professor telling me a story about how a census taker came to his house to ask him some questions. One of the questions he asked was:

"How many children do you have, and what are their ages?“

The professor answered:

"I have 3 children, their ages multiply to 36, and their ages add to the house number of the house next door.“

The census taker walked next door, came back and said:

"I need more information.“

The professor replied:

"I have to go, my oldest child is sleeping upstairs.“

Census taker:

"Thank you, I now have everything I need.”

How did the census taker know their ages? What are the ages of each of the three children?

Puzzle 6Tokyo is famous for it’s Tsukiji fish market. One day whilst dodging all the fish being flung around by the fish mongers I came across a sushi chef who was preparing a fish for a sushi roll. I asked him what fish it was and he said that it was the infamous Fugu (Poisionous Pufferfish). This fish was quite small but I asked him how big the biggest Fugu was that he had caught. He said that there are separate parts of a Fugu; the head, body and tail. He said that the head was 9cm long,it’s tail was as long as the head and half it’s back and it’s back is as long as the head and tail together.

HOW LONG WAS THE FISH?

Puzzle 7Over Christmas I got an email from my old university professor. In it he explained a very simple problem and asked if I could find a solution for it. This seemingly simple problem at first look is actually quite difficult when you look at it closer; it is not all it seems! It’s based on a ‘triangle’ made up of 4 different shapes. Both of the ‘triangles’ in the diagram use exactly the same pieces. They are re-arranged in different ways to get 2 different ‘triangles’.

Can you explain where the holecomes from on the bottom

‘triangle’?