Arithmetic sequences

problem

Janusz Asked

Age

16 to 18

Challenge level

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?
problem

Skip Counting

Age

5 to 7

Challenge level

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
problem

Six in a Circle

Age

5 to 7

Challenge level

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?
problem

Alphabet Blocks

Age

5 to 11

Challenge level

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
problem

The Great Tiling Count

Age

7 to 11

Challenge level

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
problem

Red Balloons, Blue Balloons

Age

7 to 11

Challenge level

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
problem

Tables Without Tens

Age

7 to 11

Challenge level

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
problem

Unravelling Sequences

Age

7 to 11

Challenge level

Can you describe what is happening as this program runs? Can you unpick the steps in the process?
problem

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?
problem

Investigating Pascal's Triangle

Age

7 to 11

Challenge level

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.