AoPS Wiki talk:Problem of the Day/June 15, 2011

Solution

Solution 1

We can solve this problem by a bit of trial and error.

We can guess she rode days and we get since the mean is clearly and there are terms.

That's a bit too small.

We can add to and get . That's still too small.

Now, we add to get , the answer we want.

We now count how many numbers are in the following list: .

Adding to the list gives us .

Dividing by gives us . Subtracting gives us .

Our list has numbers. Since she started on a Monday, we must add days. Our answer is

Solution 2

On the first day, Jenny rode miles. On the second day, she rode miles. On the third day, she rode miles.

This is the sequence which is an arithmetic sequence: first term , common difference .

We are trying to find the number of terms such that the partial sum of the sequence is .

The formula for the sum of a partial sequence is , where is the first term, is the number of terms, and is the common difference. (Try to derive it!)

Let and Then we have:

The second root is not an integer, so the workout lasted for days. The day after Monday is .