Algebra - January 2004, All Stages

Problems

Age 5 to 7 Challenge Level:

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?

The Brown Family

Age 5 to 7 Challenge Level:

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

Cherry Buns

Age 7 to 11 Challenge Level:

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?

Cherries Come in Twos

Age 7 to 11 Challenge Level:

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?

Age 7 to 11 Challenge Level:

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

Starting Fibonacci

Age 11 to 14 Short Challenge Level:

What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

Age 11 to 14 Challenge Level:

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. . . .

Turnips

Age 11 to 14 Short Challenge Level:

Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

Children at Large

Age 11 to 14 Challenge Level:

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

Sweet Shop

Age 11 to 14 Challenge Level:

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.

To Run or Not to Run?

Age 11 to 14 Short Challenge Level:

If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?

How Many Miles to Go?

Age 11 to 14 Challenge Level:

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Chocolate 2010

Age 14 to 16 Challenge Level:

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

Always Perfect

Age 14 to 16 Challenge Level:

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

Rational Integer

Age 14 to 16 Short Challenge Level:

Weekly Problem 39 - 2012
For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

Fibonacci Factors

Age 16 to 18 Challenge Level:

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