A perfect number is a number which is equal to the sum of all its factors except itself.
Successful Solvers:
Mark Hartley, Castle Hill High
John Rogers, Knox Grammar
Everybody knows that, because of Pythagoras' theorem, the diagonal of a unit square must have irrational length.
I have a problem regarding periodic decimals. It concerns a decimal such as $0.4\dot{9}$ (i.e. $0.4999\ldots$).
For a change this time, we present to you something which is strictly not a game (but is an interesting challenge).
The sum of two positive integers is $10 000 000 000$.
Q.273 What is the smallest and largest possilbe number of Fridays that can occur on the 13th of a month in any calendar year?
Q.261 In a right-angled triangle, the shortest side is $a$ cm long, the longest side is $c$ cm long and the other side is $b$ cm long. If $a,b,c$ are all integers, when does $a^2 = b+c$?