Explaining, convincing and proving

game

Yih or Luk Tsut K'i or Three Men's Morris

Age

11 to 18

Challenge level

1 out of 3

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.
problem

The Bridges of Konigsberg

Age

11 to 18

Challenge level

1 out of 3

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
problem

What Does It All Add Up To?

Age

11 to 18

Challenge level

2 out of 3

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
problem

Doodles

Age

14 to 16

Challenge level

1 out of 3

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
problem

Russian Cubes

Age

14 to 16

Challenge level

1 out of 3

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
problem

Natural Sum

Age

14 to 16

Challenge level

1 out of 3

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 × 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
problem

N000ughty

Age

14 to 16

Challenge level

1 out of 3

How many noughts are at the end of these giant numbers?
problem

Euler's Squares

Age

14 to 16

Challenge level

1 out of 3

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
problem

Our Ages

Age

14 to 16

Challenge level

1 out of 3

I am exactly n times my daughter's age. In m years I shall be ... How old am I?
problem

Mod 3

Age

14 to 16

Challenge level

1 out of 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.