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Horoscope Hijinks I (Posted on 2006-11-28) Difficulty: 4 of 5
The twelve signs of the horoscope (AQUARIUS, ARIES, and so on) run a race along the Zodiac. In how many different ways can the race end, if ties are possible?

  Submitted by Federico Kereki    
Rating: 3.0000 (1 votes)
Solution: (Hide)
If the 12 signs end as "a" signs together first, followed by "b" signs together, followed by "c" signs together, and so on, let's write it as a/b/c....

We could assume a≤b≤c... if we also take into account in how many different ways we can permute the numbers a, b, c....

The possible ways to get a/b/c... are 12!/a!b!c!... multiplied by the number of ways to order a, b, c...

For example, with 1/2/2/7, the number is 12!/1!2!2!7! times 4!/1!2!1!.

Summing over the 70 possible combinations of a/b/c..., we get the final answer: 28,091,567,595.

Note: Looking around in the web, I found the first problem (with 8 horses instead of 12 signs) and a different way of solving it at "Nick's Mathematical Puzzles".

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Answer K Sengupta2023-09-21 10:55:09
Some ThoughtsPuzzle Thoughts K Sengupta2023-09-12 00:07:34
re(3): Smaller ZodiacsJoel2006-11-28 16:19:08
re(2): Smaller ZodiacsCharlie2006-11-28 16:08:21
re(2): Smaller ZodiacsJoel2006-11-28 16:03:33
SolutionCan this be done without a computer? -- computer solutionCharlie2006-11-28 16:00:11
Solutionre: Smaller Zodiacstomarken2006-11-28 15:42:45
re: Smaller Zodiacs (missing option)Steve Herman2006-11-28 15:40:05
Some ThoughtsSmaller ZodiacsJer2006-11-28 15:11:31
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