Secondary Students' Solutions

Take a look at these recently solved problems.

Subtraction Surprise

Age 7 to 14

Challenge Level Yellow star

Try out some calculations. Are you surprised by the results?

Non-transitive Dice

Age 11 to 14

Challenge Level Yellow star

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Pair Products

Age 14 to 16

Challenge Level Yellow star

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Pick's Theorem

Age 14 to 16

Challenge Level Yellow star

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Square Remainders

Age 16 to 18

Challenge Level Yellow star

What is the remainder if you divide a square number by $8$?

Divisible Factorisations

Age 16 to 18

Challenge Level Yellow star

Can you show that $n^5-n^3$ is always divisible by $24$?

Proper Factors

Age 16 to 18

Challenge Level Yellow star

Can you find the smallest integer which has exactly 426 proper factors?

Square Difference

Age 16 to 18

Challenge Level Yellow star

Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?

Sissa's Reward

Age 11 to 14

Challenge Level Yellow star

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

Square It

Age 11 to 16

Challenge Level Yellow star

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Parallelogram It

Age 11 to 16

Challenge Level Yellow star

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

Rhombus It

Age 11 to 16

Challenge Level Yellow star

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Calculating with Cosines

Age 14 to 18

Challenge Level Yellow star

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?