# Pattern IQ Task

I'm looking for solution & explanantion for following pattern riddle: Intuitively I guess that that should be C but I don't see a clear argument.

## 3 Answers

Let's number the nine fields with numbers 1 through 9, beginning with 1 in the upper left corner, then going left to right first, up and down second. So 1 is the upper left field, 3 is the upper right one, the '?' is 8 and the empty one is 9.

Let's refer to the checkered squares as square #1, square #2, etc. accordingly. So the one we need to find is square #8, the '?'.

Let's number the nine colored fields within each checkered squares in the same way.

Now. We need to deduce any kind of construction rule. We can make the assumption that

each square is constructed from the square directly above it, with the same construction rule per row. - I'll explain below where that assumption comes from.

It's an assumption rather by exclusion than by direct hint, but it is not contradicted by the puzzle. If it properly leads to an available answer, that would be at least a correct solution, although there might more than one.

So that means for a first step that

each square in the middle row was constructed from the square above it by the same rule.

For instance

Mirroring each square on its diagonal line that goes from up left to bottom right would do it.
But the exact rule is not important, since we will look for a new rule to go from the middle row to the bottom row. It only establishes the initial assumption.
Actually, you'll probably first spot that this rule exists, then make it your assumption that this is the general construction rule for this puzzle. This is how I deduced my solution, I just presented the derived assumption as initial assumption to streamline the explanation.

So once that's established, we now need to come up with

a new rule that will construct all squares in the bottom row from the ones above them in the middle row. We have one example in fields 4 and 7, so let's take a look at the transition from square #4 to #7.

We find that

To arrive from square #4 at square #7, we could for instance invert its colored fields 3, 4, 6 and 7. You might come up with a different description that has the same result as my inverting colors approach, but it would essentially lead to the same rule.

If you then

apply the same construction rule to square #5, inverting the colors 3, 4, 6 and 7 of square #5, you'll end up with solution E for square #8.

So, the initial assumptions lead to a logical way to arrive at one of the available solutions. Might not be the only one, but it's one that works.

BTW, square #9

would have 7 black color fields resembling the letter H. It's not offered as available solution.

I think answer is

D.

Explanation:

Assign numerical value to each square, 1-9, left to right, descending order.Add the white squares. In first column the sum of each is equal to 20. In third column the sum of each equals thirty which is why the last isnt needed. Its extraneous. In second column the value of the first is 39. The value of box underneath is 33. 6 less. So the value underneath that should be 27. 6 less. D is equal to 27.

Try it with

adding the black squares. All boxes in first column equal 25. Third column equals 15. First box in second column is 6. The box underneath is 12. The one underneath should be 6 more which is 18. Which is also D.

• Guy, welcome to Puzzling.SE! The spoiler markups are done using >! for future reference! – El-Guest Sep 30 '18 at 23:27

This question doesn't look as if it has enough information for a satisfactory answer, so:

leave it blank. The reason is that this is not an option is because you can't see it!