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## Glue Factory Stakes

 Category: Logic-Grid Submitted By: cnmne Fun: (2.86) Difficulty: (3.27)

Five horses have just competed in the annual "Glue Factory Stakes". With the given clues, determine for each horse: its color, its number, its jockey, and where it finished.

Finish: Win, Place, Show, 4th, 5th
Horses: Ghoulish Pleasure, Infirm, Roughage, Seattle Slow, Secret Harriet
Colors: Black, Red, Yellow, Blue, White
Numbers: #18, #29, #37, #46, #50
Jockeys: Allen, Jerry, Luke, Nathan, Tim

1) The 5 horses are: Infirm, the horse ridden by Tim, the horse that wore black, #50, and the horse that Placed.
2) The 5 jockeys are: Allen, the one that rode Seattle Slow, the one that rode the horse that wore red, the one that rode #18, and the one that rode the horse that Showed.
3) Secret Harriet finished ahead of the horse that wore blue, which finished ahead of the horse ridden by Luke.
4) #50 finished ahead of the horse that wore white, but finished behind Roughage.
5) Jerry finished next to #37.
6) Allen finished next to #29.
7) The horse that wore blue finished two positions away from #50.
8) The horse that wore yellow finished two positions away from #46.
9) Luke finished at least two positions away from #46.
10) Nathan finished at least two positions away from #50.
11) Luke rode a horse that wore an even number.
12) Only one of the horses that wore a primary color also wore an even number.

Much of the grid can be filled using the normal process of elimination. The following explanation resolves one of the more difficult sections.

If #46 finished 5th, then the horse that wore yellow would have had to Show (clue 8), and Luke would have had to have ridden the horse that Showed (clues 3 and 9). This would mean that Luke rode the horse that wore yellow, which Showed. The horse that Showed could not wear #18 (clue 2) or #50 (clues 3, 4, and 7); Luke could not wear #37 or #39 (clue 11) or #46 (clue 9); therefore, Luke could not have ridden the horse that Showed. Thus, #46 could not have finished 5th, which means that #18 finished 5th.

Win: Secret Harriet, Black, #46, Allen
Place: Seattle Slow, Blue, #29, Nathan
Show: Roughage, Yellow, #37, Tim
4th: Ghoulish Pleasure, Red, #50, Jerry
5th: Infirm, White, #18, Luke