December 7, 1998
Problem of the Week

Santa's Pack Held Thirty Toys   from Reader's Digest



Try this poetic puzzle involving 5 elves, dressed in 5 different colors, who made 5 different types of toys.
  1. Ole Santa's pack held thirty toys
  2. Made by his elfin crew;
  3. And though none made the same amount,
  4. Each elf made more than two.
  5. The elf named Cher made one more toy
  6. Than the elf who dressed in reds,
  7. But Cher made one less Christmas toy
  8. Than the elf who made the sleds.
  9. Spry Johnny elf made racing cars;
  10. Five toys were made by Jane.
  11. The elf who dressed in yellow suits
  12. Made each and every train.
  13. The elf who always dressed in green
  14. Made one-third as many as Sue.
  15. Cute Marcia elf was dressed in orange,
  16. And one elf dressed in blue.
  17. The elf who made the spinning tops
  18. Made the most toys of them all.
  19. Another perky, smiling elf
  20. Made each and every ball.
  21. Ole Santa's pack held 30 gifts
  22. All tagged for girls and boys.
  23. From the clues that you've been given,
  24. Now guess who made what toys.


Solution to the Problem:

Each elf made at least three toys (line 4). One elf made three times as many as another (13-14), and three elves made consecutive amounts (5-8). If you eliminate duplicate amounts (3), two possible number combinations total 30: 12/6/5/4/3 or 9/7/6/5/3.

With either solution, Sue made the most (13-14). And we know that she made tops 17-18). She was not dressed in green (13-14), orange (15), red (5-6), or yellow (11-12), so she must be the elf in blue.

The two elves who made the least must be dressed in green (13-14) and red (5-6). Therefore the elf who made the least can not be Marcia (15). It also can not be Cher (5-8), or Jane (10), so Johnny must have made the least. And he made cars (9).

The elf who made the second most was not Jane (10)or Cher (5-8), so it must have been Marcia.And Marcia dressed in orange (15).

Since the two elves who made the least were in green and red, the elf in yellow must have made the third-smallest amount of toys. And that elf made trains (11-12).

Since the elf making sleds could not have made the second-smallest amount of toys (7-8), Marcia must have made the sleds. Cher is therefore the elf in yellow, and the person who made the second-smallest amount of toys is in red (5-8).

By elimination, Johnny is in green, and Jane is in red and made the balls. Since the elf in green made three toys, Sue must have made nine toys (13-14), and our amounts of toys must be: 9/7/6/5/3.

Sue (blue) made 9 tops.
Marcia (orange) made 7 sleds.
Cher (yellow) made 6 trains.
Jane (red) made 5 balls.
Johnny (green) made 3 cars.



Correctly solved by:

1. Darren Rennie Winchester, VA
2. Devin Grim Winchester, VA
3. Jeremy Ramsey Winchester, VA
4. John Beavers Winchester, VA
5. Michael Leatherman Norfolk, VA
6. Elizabeth Dyke Winchester, VA
7. Krista Ramey Winchester, VA
8. Rachel Rasmussen Winchester, VA


Send any comments or questions to: David Pleacher