Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Clement from Sha Tin College in Hong Kong has sent in this
solution for Scoring with Dice:
For the first question, I had to find a combination using 4
numbers, and its product had to be 4 times its sum. I first tried
to find a suitable number, with many factors. And it had to be big
enough in order to fit the sum of the combination in.
I thought: 40 would probably be too small to fit the sum of the
combination in and 44 only had 4 factors, so I tried 48. I listed
all the factors: 2*24, 3*16, 4*12 and 6*8 and tried splitting each
one of them into 4 steps, such as: 2*6*4*1 or 3*4*2*2 and I
eventually came up with one: 6*2*2*2, the sum being 12.
I used the same method for the next two questions and came up
with 5*3*2*2 which made 60, the sum being 12 and 3*3*2*2*2 which
made 72, the sum being 12.
Thank you for this clearly explained answer Clement.