As a warm-up, try to solve the
Lo Shu,
the 3×3 magic square using numbers 1-9. Each of the 8 lines adds up to 15. Puzzle D is an example of
a
graceful graph. A harder problem is
the
Kelvin conjecture:
if the soap bubbles in a froth each contained equal amounts of air, what would they look like? Turns out the bubbles
would look like
Weaire-Phelan foam.
At the Beijing olympics, the
Water Cube is
actually a large scale mathematical sculpture based on Weaire-Phelan foam. Other 8-related magic: the
24-cell has 6(2^19 ยท 5688888889 + 347) distinct
nets, 3778888999 has
multiplicative persistence 10,
and the
squares of 6666667, 665949276513522,
and 9949370777987917 are all interesting.