Algebra - January 2004, Stage 3&4

Problems

Starting Fibonacci

Stage: 3 Short Challenge Level:

Weekly Problem 40 - 2012
What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

Turnips

Stage: 3 Short Challenge Level:

Weekly Problem 37 - 2012
Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

Stage: 3 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. . . .

To Run or Not to Run?

Stage: 3 Short Challenge Level:

Weekly Problem 38 - 2012
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?

Children at Large

Stage: 3 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

Stage: 3 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.

How Many Miles to Go?

Stage: 3 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

Stage: 4 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

Stage: 4 Challenge Level:

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

Integer and Integer

Stage: 4 Short Challenge Level:

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