# What's the missing tile?

A friend sent me this a few days ago, and I'm usually quite good at figuring them out. But this one is driving me crazy, so I thought maybe some of you would like to have a go. I have a hunch about the answer, but I'm really not sure...

The inner shape must be

a square,

because

this creates symmetry: reading along the rows one by one gives "triangle, square, square; square, circle, square; square, square, circle/pentagon1", as does reading down the columns one by one.

1 The shading in the bottom right cell makes it very hard to tell whether the inner shape is a circle or a pentagon.

Altogether there are three elements we need to fix: the inner shape, the outer shape, and the colour/shading between. In order for the solution not to be discoverable by only fixing two of these elements, it must be

A, which has both inner and outer shape in common with D, both inner shape and shading in common with E, and both outer shape and shading in common with B.

This is confirmed by the fact that

on your image, the checkbox for A is highlighted in a different colour from the others.

• That was my hunch too, I just wasn't sure because three big circles in a row seems odd, but the logic is sound. I wouldn't read much into the different shading around A, I think the reason for it is just because it's the first answer, and prompt you to select one... I can't confirm though, I don't know what site this came from. I only got an image! – Mark Oct 8 '16 at 14:31
• @Mark Maybe the logic works columnwise rather than rowwise, so that the fact that there are three big circles in a row is just because three different starting points yielded big circles after 2 steps. – Rand al'Thor Oct 8 '16 at 14:39
• The last inner shape isn't a circle, it's a pentagon. – bill bsl Oct 8 '16 at 16:24
• @Tyler I magnified the image and I'm still not sure. You could be right, but the diagonal lines between the inner and outer shapes make it very hard to be certain. Anyway it doesn't affect my argument :-) – Rand al'Thor Oct 8 '16 at 16:31
• I'm pretty sure it's a pentagon on the inside... But good point about the vertical logic, I hadn't considered that as much... I thought it'd have to add up every way.. – Mark Oct 8 '16 at 17:19

The missing outer shape must be

a circle, because each vertical column has two outer circles.

The missing inner shape must be

a square, because each vertical column has two inner squares.

/////, because each horizontal row's shading is symmetric around the center. (The alternative would be \\\\\ because first and last items in each row are the same, but none of the answers offer that style shading.)

Thus we know the correct answer is

(A), the only working choice by these rules.

Pattern 1:

Row 1 and 2 have two grey shaded shapes & one different

Deduction 1:

The shape should to be grey shaded

Pattern 2:

Both rows have two same inner shapes & one different

Deduction 2:

The inner shape should to be either a square or a pentagon

Pattern 3:

Diagonals have only circle as outer shape

Deduction 3:

The outer shape should to be circle