# Where each photograph is hung is fully determined if which one of the following is true?

on June 9 at 08:43PM

Why not C?

If we put I in second we can figure out placement for the other photographs

Shunhe on June 15 at 02:50PM

Hi @Stephanie,

Thanks for the question! So let’s take (C) and say we put I in second. Well, we know that L and I must be next to one another. So let’s say we put L in the first block. Then that forces F in the last block (since F has to be in the first or last slot), and M in the third block (since M has to be in the first three slots). Then we need to put HGK somewhere, so we can put them on slots 4, 5, and 6. Then we end up with

L I M H G K F

which, if you double check, does not violate any of the rules.

Is this the only possibility? Let’s say we put L in the third block. Then that forces M into the first block (since it has to be in the first three slots), and that forces F into the last slot (since it has to be in the first or last slot). Again, we put the HGK block in 4, 5, and 6. This gets us

M I L H G K F

Which, if you compare again to the rules, doesn’t violate them. That means that we can’t completely determine where each photograph is hung by putting I in the second slot, since there are two possibilities.

Hope this helps! Feel free to ask any other questions that you might have.