# Books on a bookshelf

On a shelf the blue book is to the right of the red book, the yellow book is in one end, the black book is just before the white and the green is between blue and white. What is the order of the green book from left to right?

a. 2nd
b. 3rd
c. 4th
d. 5th
e. The problem has no logical solution

Another problem that seems to have more than one solution. I believe the problem lies in the placement of the yellow book, since we may have:
yellow | red | black | white | green | blue (5th) or
red | black | white | green | blue | yellow (4th)
Source

E) You are correct, there is no logical solution

Lets split it up and make deductions:

• The blue book is to the right of the red book

• The yellow book is in one end

• The black book is just before the white

• The green is between blue and white

- Blue cannot be first, red cannot be sixth
- Yellow is first or sixth
- Black is not sixth, white is not first, black and white adjacent
- Green is not first or sixth, blue and white two apart.

Also note:

It must go Black-White-Green-Blue or the black cannot be before white.

So, we know a chain of four, lets look at the other two:

Red is to the left of blue, and yellow is at an end. Red must therefore be adjacent to black:
Red-Black-White-Green-Blue

Yellow is 1/6, however

There is no information about where it could go, and as you show it could go on either end. Therefore green is 4/5 as you say and there is no solution.

• Does the fact that there is a solution, but not just one, imply that there is no logical solution? Commented Jan 2, 2021 at 19:58
• @gmn_1450 yes, a logical solution implies that there is a single solution, that can be derived logically. Neither of the answers can be shown to be the right one with logic, therefore no logical solution. Commented Jan 2, 2021 at 19:59
• Hmm ... interesting. I did not imagine that something similar to the excluded third principle for propositions would apply in a case like this. Thanks. Commented Jan 2, 2021 at 20:01
• So ... a logical solution besides being derived logically (obviously) must be unique. Commented Jan 2, 2021 at 20:03
• @gmn_1450 depends on the context, but for puzzles yes. Both of the possibilities are technically 'logical solutions' as we have reached them via logic, but as this is known to be a logic puzzle, it can be inferred that there should be one solution. We can actually confirm this, as we know it must be on of a-e, and it cannot be determined which of the numbers it is, therefore must be e), and we then know that here, the logical solution is unique in this context Commented Jan 2, 2021 at 20:06