From New Scientist #1696, 23rd December 1989 [link]
Amy, Beth, Jo and Meg decided to give each other pots of marmee-lade for Christmas. Each girl made a number of pots and then divided her pots into three piles, which were not necessarily equal; then she wrapped up each pile, labelled each parcel, and put them under the Christmas tree. The total number of pots involved was between 50 and 100.
We will let the letters A, B, C, …, I stand for the digits 1, 2, 3, …, 9 in some order. Amy gave D/F of her pots to Jo, and C/B to Meg. Beth gave H/G of her pots to Amy, H/A to Jo, and D/G to Meg. Jo gave F/G of her pots to Amy. Meg gave A/B of her pots to Beth, and D/H to Jo.
On Christmas day, each girl opened the three parcels she had received. Amy received H/E of her pots from Beth, and F/E from Jo. Jo received D/I of her pots from Amy, D/H from Beth and D/A from Meg.
Note that all the fractions were in reduced form before letters were substituted (1/2 and 2/3 are in reduced form, whereas 4/8 and 6/9 are not).
What was the total number of pots that were given?
This puzzle completes the archive of Enigma puzzles from 1989. There is now a complete archive of New Scientist puzzles from July 1975 to December 1989, and from February 1998 to December 2013, a total of 1553 puzzles. There are 423 Enigma puzzles remaining to post.