The Missing Weekly Puzzle

Shoe Box Scramble

Shoe Box Scramble is a flawed combination of two common logic puzzles (which could be why this puzzle hasn't been unlocked)

Typically, the first version of the puzzle states that three closed boxes each have a different item inside and that each box has been mislabeled by someone

This puzzle goes on to ask how many boxes need to be opened in order to figure out which item is in each box (the answer being that you only need to open one box)

A second version of the puzzle has three closed boxes with one box containing two of the same item, another box having two of a different item and the third box containing one of each item

This second puzzle adds the condition that you may only remove (or look at) one item from any box and asks which box you should remove the item from (the answer being the box labeled as mixed since this is the only box where you can be certain of what both shoes are just by looking at one shoe)

Now here's what the weekly puzzle would've been



The letters on the box signify the shoes inside the box. "R" stands for right shoe and "L" stands for left shoe. However, some careless clerk put the wrong label on each of the three boxes. In order to figure out the contents of all three boxes, you only need to open one of them. Which one should you open?

The configuration of the boxes is set up for the second version of the puzzle while being able to open any box to see what's inside relates to the first version of the puzzle

By asking which box you should open, the question should've specified that you may only remove one shoe from any box

Layton's Solution

That's right. The key here is that each box is mislabeled. For example, if you open the box marked RL and find two right shoes inside, you know that box is actually the RR box. Furthermore, the box marked LL can't contain LL because all boxes are mislabeled, nor can it be the already open RR box. Therefore, it must be the RL box. Now the final box's contents should be obvious. Even if you find two left shoes instead of right shoes in the RL box, the process for solving this problem doesn't change.

Layton's solution talks about just opening a box to see both shoes inside (the first version of the puzzle) and uses the RL box as an example (the box that would've been the only correct answer for the second version of the puzzle)

Neither the question nor the solution can decide which version of the puzzle it wants to be and ends up being a flawed puzzle

The solution referring to the RL box as being an example of which box to open (not the box that must be opened) indicates that the answer should be that you only need to open one box, but this can't be the answer since it's part of the question

Even if the solution indicated that the RL box must be opened, this can't be the answer either since by being able to open a box to see both shoes inside (as implied by the question and stated in the solution), you can open any of the three boxes to figure out the contents of the other two