Find a great variety of ways of asking questions which make 8.
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
What is the least square number which commences with six two's?
If you can't at first see how to do this with six twos try three
twos. Clearly 222 is not a perfect square. There is no whole number
between the square root of 2220 and the square root of 2229 but 149
lies between the square root of 22200 and the square root of
This was solved by Ling Xiang Ning, Allan, age 13 from Raffles
Institution, Singapore and Tony Cardell and John Lesieutre, age 14
from State College Area High School, Pennsylvania, USA.
Here is Allan's solution: First I try 222222. It is not a square
Next, I try 2222220 and 2222229. I take the square root of both
of them and find out that there is no square number between
Next, I try 22222200 and 22222299. I take the square root of
both of them and find out that there is no square number between
I try 222222000000 and 222222999999. I take the square root of
both of them and find out that there is one square number between
them. This number is the square of 471405 which is
So the least square number starting with six twos is