A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain?
The number of cans in each row form an arithmetic sequence, with first term 1 and common difference 2.  If there are $n$ terms, then the terms are 1, 3, $\dots$, $2n - 1$.

The total number of cans is therefore the sum of the arithmetic series \[1 + 3 + 5 + \dots + (2n - 1).\]The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum is $[1 + (2n - 1)]/2 \cdot n = n^2$.

Then from $n^2 = 100$, we get $n = \boxed{10}$.
10
Level 3
Algebra
Problem: A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the number of rows in the display, we need to establish a pattern for the number of cans in each row. The first row has 1 can. Each subsequent row has 2 more cans than the previous row. Therefore, the number of cans in each row can be expressed as follows:

- Row 1: 1 can
- Row 2: 1 + 2 = 3 cans
- Row 3: 3 + 2 = 5 cans
- Row 4: 5 + 2 = 7 cans
- Row 5: 7 + 2 = 9 cans
- Row 6: 9 + 2 = 11 cans
- Row 7: 11 + 2 = 13 cans
- Row 8: 13 + 2 = 15 cans
- Row 9: 15 + 2 = 17 cans
- Row 10: 17 + 2 = 19 cans

We can see that the number of cans in the nth row can be represented by the formula: 
C(n) = 1 + 2(n - 1) = 2n - 1.

To find the total number of cans in r rows, we need to sum the number of cans in each row from 1 to r:
Total cans = C(1) + C(2) + ... + C(r) = (2(1) - 1) + (2(2) - 1) + ... + (2(r) - 1).

This simplifies to:
Total cans = (2(1 + 2 + ... + r)) - r.

The sum of the first r natural numbers is given by the formula:
1 + 2 + ... + r = r(r + 1)/2.

Substituting this into the total cans equation gives:
Total cans = 2(r(r + 1)/2) - r = r(r + 1) - r = r^2.

We set this equal to the total number of cans, which is 100:
r^2 = 100.

Taking the square root of both sides, we find:
r = 10.

Thus, the display contains 10 rows.<|END_OF_LATENT|> The final answer is $10$.