Exploring and noticing

problem

Newspaper Sheets

Age

14 to 16

Challenge level

2 out of 3

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
problem

Collatz-Ish

Age

14 to 16

Challenge level

2 out of 3

A sequence is generated using these rules. For which values of n is the nth term equal to n?
problem

Back in Time

Age

14 to 16

Challenge level

2 out of 3

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?
problem

Oldest and Youngest

Age

14 to 16

Challenge level

2 out of 3

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?
problem

Just Rolling Round

Age

14 to 16

Challenge level

3 out of 3

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
problem

There's Always One Isn't There

Age

14 to 16

Challenge level

3 out of 3

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
problem

Guessing the Graph

Age

14 to 16

Challenge level

3 out of 3

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
problem

Can You Traverse It?

Age

14 to 18

Challenge level

1 out of 3

How can you decide if a graph is traversable?
problem

Flipping Twisty Matrices

Age

14 to 18

Challenge level

1 out of 3

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
problem

Road Maker

Age

14 to 18

Challenge level

1 out of 3

Which of these roads will satisfy a Munchkin builder?