Clara knocks over the two stacks of blocks shown in the diagram. She then uses the blocks to build a similar stack whose top layer has one block and each layer below has one more block than the layer above it. If she builds the largest possible stack, how many blocks will be left over?
![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-099.jpg?height=254&width=468&top_left_y=1735&top_left_x=1294)
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Solution 1

The first stack is made up of $1+2+3+4+5=15$ blocks.

The second stack is made up of $1+2+3+4+5+6=21$ blocks.

There are 36 blocks in total.

We start building the new stack from the top.

Since there are more than 21 blocks, we need at least 6 rows.

For 7 rows, $1+2+3+4+5+6+7=28$ blocks are needed.

For 8 rows, $1+2+3+4+5+6+7+8=36$ blocks are needed.

Therefore, Clara can build a stack with 0 blocks leftover.

## Solution 2

Since the new stack will be larger than the second stack shown, let us think about adding new rows to this second stack using the blocks from the first stack.

The first stack contains $1+2+3+4+5=15$ blocks in total.

The first two rows that we would add to the bottom of the second stack would have 7 and 8 blocks in them, for a total of 15 blocks.

This uses all of the blocks from the first stack, with none left over, and creates a similar stack. Therefore, there are 0 blocks left over.

ANSWER: (A)