Question in Image Below         Solution 22) Fact   Perfect Squares can only have last digits 0, 1, 4, 5, 6, 9   Perfect Square CANNOT have these last digits: 2, 3, 7, 8 If (i) and (ii) were true, a number with last digit 2 is a perfect square, impossible!...

SASMO Question in Image below     Solution   21) Notice that   9 = 10 – 1   99 = 100 – 1   999 = 1000 – 1   . . .   999…999 (2017 digits) = 10^2017 – 1   So   A = (10^1 + 10^2 + 10^3 + …...

Using the  Chinese Remainder Theorem to find the Last Five Digits of 15^2015 (SASMO Math Olympiad Problem) .   Question and Solution are in Images attached.   Question             Solution                    

Question and Solution in Images Note: A SASMO 2018 Sample for a senior secondary school Math Olympiad. A Geometry Math Olympiad Problem. Find AE + EC as a geometrical invariant concept.