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Math and Logic

How Do They Fit?

The two puzzle pieces below fit into the 3 x 3 grid without rotation or reflection:

Based on these two clues

  1. G is south of J

  2. K is east of F,

where is E located? Keep reading to find out, or skip straight to today's challenge for a similar but tougher problem.

Let's look at both clues and determine which condition is harder to satisfy. To satisfy

G is south of J,

the EFG piece needs to be in the bottom two rows of the grid. There are two ways to do this:

To satisfy

K is east of F,

the JKL piece needs to be in the far right column. There is only one way to do this, so let's place the JKL piece first:

Now we can place the EFG piece so clue 1 is also satisfied. This puts E in square C1:

The three puzzle pieces below also fit into the 3 x 3 grid without rotation or reflection:

Based on these clues

  1. Y touches both F and G (touching diagonally is ok)

  2. E is south of G

  3. H is east of Z,

where is H located?

Clue 2 means that the EF piece must be in the lower two rows and the GH piece is in the top two rows:

Meanwhile, clue 1 tells us that the YZ piece is in the middle column. There are two ways this can happen:

From clue 3, we know that the GH piece must be in the right column. This means the solution is the figure on the left, which puts H in square B3.

The puzzle below is a bit more complex. Instead of looking at the three clues separately, think about how they might conflict.

Today's Challenge

The three puzzle pieces below fit into the 4 x 4 grid without reflection or rotation:

Based on these clues, where is J located?

  1. F is farther east than V.
  2. E touches Z (they can touch diagonally).
  3. J is in a row below X's row.

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