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?
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
Can you explain the strategy for winning this game with any target?
Well done all of you who found that Ewa had
301 eggs and Tomek should pay him £23.83
Quek from Tao Nan School, Singapore, Nicholas
and Oliver from Clevedon Community School in North Somerset and
Rachel from Hethersett High School in Norwich all used the lowest
common multiple of 2, 3, 4, 5, and 6, namely 60 and then used the
60 times table.
This is Quek's reasoning:
60 * 2 + 1=121
60 * 3 + 1=181
60 * 4 + 1=241
60 * 5 + 1=301
301 * 95/12 p = 2382p + 11/12 p
Tomek should offer to pay £23.83.
Amy of Hethersett High School, Norwich, used a
similar method to this one from Emma and Elizabeth of Ipswich High
We wrote out the multiples of 7. We realized that if it was
divisible by 5 with a remainder of 1 then it must end in 6 or 1. We
also realized that if it was divisible by 2 with a remainder of 1
it must end in a 1. We went through the multiples of 7 and picked
out those ending in 1 and checked them for divisiblity by 3 with
remainder of 1 and came up with 301.
A slightly different approach, also starting
with multiples of 7, was used by Laura, and Amelia of Ipswich High