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A 6x6 block

The answer book of this puzzle book says that the first five are all consistent but the last one is not because the Z has to be a U. I can't seem to agree with this as U seems to be attached to N, P, E, L & Z. Clearly it can only be attached by four ends adjacent wise..

If PUL*, then N and Z must be on the top and bottom. Third&fourth in agreement. And first. Wouldn't this mean the 2nd and 6th are the odd ones out?

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  • $\begingroup$ (1) If you’re quoting a puzzle that you didn’t create, you must say where you got it. (2) Can you elaborate what you mean by “a consistent view with 1 or more that is 'odd'”? $\endgroup$ – Peregrine Rook Jun 9 '17 at 0:22
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I'm going to use directions here in relation to the letter's perspective, so something described as "above" a U means it is on the side adjacent to the "top" of an upright letter U.

Additionally, I'll use numbers to describe the dice (left to right) so P1 refers to the P on the first die, while L5 would refer to the L on the fifth die.

First pair of consistent dice:

The first and fourth are consistent, as they are basically a rotated view of the same three sides. Note that in the first the side that looks like an N ends up looking like a Z in the fourth, due to the orientation. In both of these, the U side has a P "below" it and the Z/N to the "left" of the U. So we can ignore the fourth, for now.

Second pair of consistent dice:

The third and fifth dice are similarly consistent, as there is an L to the "left" of the U and a Z/N "above" the U. The orientations of all letters are correct, so we'll ignore the fifth die.

What about those two pairs compared to each other?

But notice that the U3 cannot be the same as U1, as U1 has an N/Z to the left and U3 has an L to its left. So either these two pairs are inconsistent, or they are showing two different letter U's on the die.

One of the remaining two:

Now, U2 has an L "above" it. This means U2 can't correspond with U3, but it can correspond with U1. This would put L2 opposite P1 and an E2 opposite N/Z1. For die 3 to be consistent, U3 can be opposite U1, and have N1 "above" it.

And the last one?

This puts a U to the "left" of P1, which is inconsistent with P6, so P6 is the only one that doesn't fit with the rest.

Why this one is tricky (in my opinion):

The trick to this puzzle is that you end up assuming the letters are P-U-N-Z-L-E when in reality they are P-U-U-Z/N-L-E.

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  • $\begingroup$ I'd love to see a die map to aid in your explanation. $\endgroup$ – feelinferrety Jun 9 '17 at 14:50
  • $\begingroup$ I would too! Sadly, didn't have time to put it together. If I have time to add something over the weekend I will. $\endgroup$ – Duncan Jun 9 '17 at 16:53
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(Solved independently; solution agrees with @Duncan's.)

First I realized N and Z could be the same; this means we know there are five distinct characters on the cube — P, U, N/Z, L, E — so the sixth face could be (and likely was) a duplicate character.

• I took a physical cube and applied letters to 3 faces to match the first image.
• Second image is ambiguous; the U could be the same as that in image 1, or could be a different one elsewhere on the cube.
• Third image for sure is a different U - to its immediate left is an L, whereas image 1 shows its U has to its immediate left an N.

We now know there are two Us, so we now know all six faces: P, U, U, N/Z, L, E

• That means the Z must be the N from Image 1, which means the second U goes to the immediate left of the N and is rotated so it opens toward that N, and the L goes to this second U's immediate left, as shown in Image 3.
• Now we know where the L is so we can place the E "below" the L and opening away from it, as shown in Image 2.

We have now placed all six faces.

Image 4 is a reoriented version of Image 1, and can trivially be found on the cube.
Image 5 is a reoriented version of Image 3, and can trivially be found on the cube.
Image 6 is not consistent, as originally noted.

Here is a layout of the cube:

enter image description here

If you rotate the entire layout clockwise 90° you see the E and the sideways P from Image 6, and see that the face "above" them is a U and not the Z shown in Image 6.

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