## Monday, November 14, 2005

### Only four blocks to solve

Molly has a set of four alphabet blocks. Each side of these blocks is printed with a different letter, making 24 in total. Molly notices that by rearranging the blocks, she can spell each of the following words:

BOXY, BUCK, CHAW, DIGS, EXAM, FLIT,
GIRL, JUMP, OGRE, OKAY, PAWN, ZEST

The Question: Which letters are on each block?

This should take just about forever to solve.

1. The four blocks:

B-A-J-S-R-F
C-O-M-N-I-Z
P-X-K-H-G-T
W-U-Y-E-D-L

2. Now that is what I call a puzzle. Nice work there.

3. From the word EXAM, we conclude that E and A are not on the same block.
From the word OGRE, we conclude that E and O are not on the same block.
From the word OKAY, we conclude that A and O are not on the same block.
Combining these, we conclude that A, E, and O are on different blocks. Assume that A is on block 1, E is on block 2, and O is on block 3.

From the words BOXY and EXAM, we conclude that X is not on the same block as A (block 1), E (block 2), and O (block 3), so X is on block 4.
From the words BOXY and OKAY, we conclude that Y is not on the same block as A (block 1), O (block 3), and X (block 4), so Y is on block 2.
From the word EXAM, we conclude that M is not on the same block as A (block 1), E (block 2), and X (block 4), so M is on block 3.
From the word OKAY, we conclude that K is not on the same block as A (block 1), Y (block 2), and O (block 3), so K is on block 4.
From the word BOXY, we conclude that B is not on the same block as Y (block 2), O (block 3), and X (block 4), so B is on block 1.
From the words BUCK and JUMP, we conclude that U is not on the same block as B (block 1), M (block 3), and K (block 4), so U is on block 2.
From the words PAWN and JUMP, we conclude that P is not on the same block as A (block 1), U (block 2), and M (block 3), so P is on block 4.
From the word JUMP, we conclude that J is not on the same block as U (block 2), M (block 3), and P (block 4), so J is on block 1.
From the words CHAW and BUCK, we conclude that C is not on the same block as A (block 1), U (block 2), and K (block 4), so C is on block 3.
From the words CHAW and PAWN, we conclude that W is not on the same block as A (block 1), C (block 3), and P (block 4), so W is on block 2.
From the word CHAW, we conclude that H is not on the same block as A (block 1), W (block 2), and C (block 3), so H is on block 4.
From the word PAWN, we conclude that N is not on the same block as A (block 1), W (block 2), and P (block 4), so N is on block 3.

Now, we must still have three letters for block 1, and two letters for each of the blocks 2, 3, and 4. We have the following letters left:

D, F, G, I, L, R, S, T, Z

From the words DIGS, FLIT and GIRL, we conclude that I is not on the same block as D, F, G, L, R, S, and T, so I is on the same block as Z. Furthermore, I and Z are on block 2, 3, or 4.
From the word ZEST, we conclude that Z is not on the same block as E (block 2), so Z is on block 3 or 4.
From the word OGRE, we conclude that G and R are not on the same block as E (block 2), and O (block 3), so G and R are on block 1 or 4, but not on the same block.
From the word GIRL, we conclude that I is not on the same block as G and R (block 1 or 4), so I is on block 2 or 3. Since Z is on block 3 or 4, I and Z must be on block 3. Now we have all six letters of block 3: C, I, M, N, O, and Z.

From the word GIRL, we conclude that L is not on the same block as G and R (block 1 and 4), so L is on block 2.
From the words FLIT and GIRL, we conclude that F, G, L, R, and T are not on the same block as L (block 2), and from the word ZEST, we conclude that S is not on the same block as E (block 2). So D must be on block 2.
Now we have all six letters of block 2: D, E, L, U, W, and Y.

From the words GIRL and DIGS, we conclude that G is not on the same block as R and S.
From the words FLIT and ZEST, we conclude that T is not on the same block as F and S.
Combining this, F, R, and S must be on the same block (block 1), and G and T must be on the same block (block 4).

Now we have all six letters of all blocks:
Block 1: A, B, F, J, R, and S.
Block 2: D, E, L, U, W, and Y.
Block 3: C, I, M, N, O, and Z.
Block 4: G, H, K, P, T, and X.

Told you it takes a long time to solve! Congratulations Bentley92!

4. I tried this one, but only figured out what each block didn't have on it. I had a whole spreadsheet. =p

5. I do that all the time when I'm trying to solve these types of things. Spreadsheets can be such fun!

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