Sunday Times Teaser 2747 – Marble Jar
by Michael Fletcher
Published: 17 May 2015 (link)
At our local fete one of the games consisted of guessing the number of marbles in a jar: some of the marbles were red and the rest were blue. People had to guess how many there were of each colour. The organiser gave me a couple of clues. Firstly, he told me that there were nearly four hundred marbles altogether. Secondly, he told me that if, when blindfolded, I removed four marbles from the jar, then the chance that they would all be red was exactly one in a four-figure number.
How many red marbles were there, and how many blue?
One Comment
Leave one →
-
Brian Gladman permalink1234567891011121314151617181920# with R red and T total marbles in the jar we have:## R.(R - 1).(R - 2).(R - 3) 1# ------------------------- = -# T.(T - 1).(T - 2).(T - 3) N## allowing N to be determined from T and Rfor T in range(400, 0, -1):a = T * (T - 1) * (T - 2) * (T - 3)for R in range(4, T):N, rem = divmod(a, R * (R - 1) * (R - 2) * (R - 3))if rem == 0 and 1000 <= N < 10000:print('{} red, {} blue, {} total'.format(R, T - R, T))breakelse:continuebreak
