Solution to Enigma No. 1551

Read the original question

Answer: X represents 14

The winner is Jet Foncannon of Philadelphia, Pennsylvania, US. There were 167 entries.

Worked answer

The fraction c (c-1) (c-2) (c-3) / (c + r) (c + r-1) (c + r-2) (c + r-3), which represents the chance of drawing four coloured balls, can be represented by N/D.

N increases in line with the sequence n(n-1)(n-2)(n-3) / 24 each time there is an extra coloured ball in the bag.

D increases in line with that sequence every time there is an extra ball in the bag (see diagram, right).

The only repeated fraction is 5/70 = 15/210 = a 1-in-14 chance.