User blog:SuperTalker101/Super's Math Problem: Week 1 Solutions

Week 1 Solutions

''This Problem of the Week is an archived version. To view the latest Problem of the Week, check the Super Math: Problem of the Week page''

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No squeezing

Method 1:

If we calculate the area required to completely cover the area of the top of SuperTalker101's tower, we find that it will take 64 1 x 1 bricks. Unfortunately, we don't have any 1 x 1 bricks. If we calculate the total area that the bricks SuperTalker101 has, we get 66. We don't have any bricks that cover 1 x 2 - the smallest brick is 2 x 2. Therefore, it is impossible to cover the top without a brick sticking out.

Method 2:

If we use trial and error, we realize that there is nearly always 4 spaces left. None of the bricks can cover such 4 spaces, so it is impossible to completely cover the top.

The Temple of Many

If we look closely, the white 2 x 4's are connected via 4 1 x 6's. This gives us 8 bricks in total.

Looking at the first layer, we see 4 more 2 x 4's connecting to form a square with a hole in it.

We realize that a 2 x 2 is in the center. Assuming we are using the least bricks as possible to make the figure possible, we add a 2 x 4 to cover the hole on back side of the second layer, then fill the hole with 2 2 x 2's.

8 + 4 + 3 = 15 bricks