# Race 5 at a Time Puzzle - Solution

## The Puzzle:

25 people enter the picnic race.

But the track is narrow and only 5 can race at a time. No one has a stopwatch.

How many races do you need to decide 1st, 2nd and 3rd?

## Our Solution:

To begin with let's race all 25 in 5 races. Imagine these are the results:

Race 1: ABCDE
Race 2: FGHIJ
Race 3: KLMNO
Race 4: PQRST
Race 5: UVWXY

Now, the three fastest could (by pure luck) have entered race 1, or perhaps race 2 etc, so the best we can say is that the 2 slowest in each race can be eliminated:

Race 1: ABC
Race 2: FGH
Race 3: KLM
Race 4: PQR
Race 5: UVW

Now let us race the winners of each race (AFKPU) and imagine we get these results:

Race 6: KFPUA

So U and A can be eliminated, plus any they have ever beaten, giving us these contenders:

Race 1:
Race 2: FGH
Race 3: KLM
Race 4: PQR
Race 5:

Since F came second in Race 6, we can eliminate the 3rd place getter in their race (as they were at least 2 places behind F so could at best be 4th overall).
Likewise since P came third in Race 6 we can eliminate the other members of Race 4.
And we don't need to race K as they are definitely the fastest, which leaves us with:

Race 1:
Race 2: FG
Race 3: (K)LM
Race 4: P
Race 5:

So one more race to decide 2nd and 3rd, imagine we get these results:

Race 7: GPLMF

And K is the winner, G 2nd, and P 3rd
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