Senior Problem - Last fortnight's answer
The Question: Remaining problem
What is the smallest positive whole number that will leave a remainder
of 2 when divided by 3, a remainder of 3 when divided by 4, a remainder
of 4 when divided by 5, a remainder of 5 when divided by 6 and a
remainder of 6 when divided by 7?
The Answer
Eeks - evil problem! I suggest starting with the biggest numbers first: try numbers which leave a remainder of 6 when divided by 7, and see which of these leave a remainder of 5 when divided by 6. Is there a pattern? This will help you move faster through the numbers until you find the answer: 419.
There is a much sneakier way to do it, which is to say that -1 is a solution, except it's not positive. So add on the lowest common multiple of 3, 4, 5, 6, 7, which is 420, and you get the answer 419.
