One of our math club leaders gave out this problem as the final problem of math club for the year. I had never seen it before, and after she handed it out, a number of math teachers were in a tizzy about finding the solution. So instead of planning for classes, we enjoyed working on this problem. But we got it! HUZZAH!
Here’s the problem:
In how many ways, counting ties, can eight horses cross the finishing line?
So we fully understand the problem, let me list all possibilities for three horses: Adam, Beatrice, and Candy. No, wait, those are better names for unicorns:
1st: A 2nd: B 3rd: C
1st: B 2nd: A 3rd: C
1st: A 2nd: C 3rd: B
1st: C 2nd: A 3rd: B
1st: B 2nd: C 3rd: A
1st: C 2nd: B 3rd: A
1st: AB (tie) 2nd: C
1st: AC (tie) 2nd: B
1st: BC (tie) 2nd: A
1st: A 2nd: BC (tie)
1st: B 2nd: AC (tie)
1st: C 2nd: BC (tie)
1st: ABC (tie)
That comes out to 13 different ways these
horses unicorns can finish the race.
That’s the answer for 3 unicorns. What’s the answer for 8 unicorns?
(FYI: If you want to know if you’re on the right track… I have 541 for 5 unicorns…)