There are 59 participants in a pie eating contest. Nadia placed third, and Johnny placed in the exact middle of all the participants. How many pie-eating participants placed between Nadia and Johnny?

One way in which to visualize this situation is to write out the first half of the 59 terms: 1 2 3 4 5, etc. The exact middle of these 59 terms is Johnny's place (30) and is the median of this set. Half of the places are to the left of 30 (1 through 29) and the other half are to the right of 30 (31 through 59).

Nadia's place is 3. The pie-eaters between 3 and 29, but not including 3 or 29, are as follows:

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

We can determine this number of participants by using the formula for an arithmetic sequence: L = F + (n - 1)D, where L and F are the last and first members of this set and D is the jump from one member to the next.

Thus, 28 = 4 + (n - 1)(1), or

28 = 4 + n - 1

This yields 25 = n

There are 25 pie-eating participants placed between Nadia and Johnny.