Algebra - January 2004, All Stages

Problems

problem icon

Weekly Problem 36 - 2012

Challenge Level: Challenge Level:1

Weekly Problem 36 - 2012

problem icon

Eggs in Baskets

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

problem icon

The Brown Family

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the information about Sally and her brother to find out how many children there are in the Brown family.

problem icon

Cherry Buns

Stage: 2 Challenge Level: Challenge Level:1

Sam's grandmother has an old recipe for cherry buns. She has enough mixture to put 45 grams in each of 12 paper cake cases. What was the weight of one egg?

problem icon

Cherries Come in Twos

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

problem icon

Beads

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

problem icon

Weekly Problem 40 - 2012

Stage: 3 Challenge Level: Challenge Level:1

Weekly Problem 40 - 2012

problem icon

Weekly Problem 39 - 2012

Stage: 3 Challenge Level: Challenge Level:1

Weekly Problem 39 - 2012

problem icon

Weekly Problem 38 - 2012

Stage: 3 Challenge Level: Challenge Level:1

Weekly Problem 38 - 2012

problem icon

Weekly Problem 37 - 2012

Stage: 3 Challenge Level: Challenge Level:1

Weekly Problem 37 - 2012

problem icon

Mind Reading

Stage: 3 Challenge Level: Challenge Level:1

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .

problem icon

Children at Large

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

problem icon

Sweet Shop

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

problem icon

How Many Miles to Go?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

problem icon

Chocolate 2010

Stage: 4 Challenge Level: Challenge Level:1

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

problem icon

Always Perfect

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

problem icon

Fibonacci Factors

Stage: 5 Challenge Level: Challenge Level:1

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

problem icon

More Beads

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

With red and blue beads on a circular wire; 'put a red bead between any two of the same colour and a blue between different colours then remove the original beads'. Keep repeating this. What happens?

problem icon

Poly Fibs

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.