¿ìè¶ÌÊÓƵ

#74 Triple digits

Set by Alison Kiddle

Using the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 once each, create three numbers – each with three digits – and find their sum.

What is the smallest total it is possible to make in this way?

What is the second-smallest total?

Is it possible to get a total of exactly 1000? If not, how close can you get?

Solution next week

#73 Square dance

Solution

For the five tiles in the first square, the proportion of area used = (total area of small squares) / (area of outside square) = 5 / 9 = 0.556. For the others, use Pythagoras’s theorem and the fact the triangles are all isosceles (with angles 90 degrees, 45 degrees, 45 degrees) to calculate the required lengths.

The side length of the second square would be 2.707, giving an area of 7.328, and the proportion used is 5 / 7.328 = 0.682.

For 10 tiles, you can imagine the central rectangle sliding diagonally until two corners touch the sides of the square. The side length of the square would be 3.707, giving an area of 13.743, so the proportion used is 10 / 13.743 = 0.728.