# Finding Sequence in Third Square

This particular puzzle is throwing me off for some reason, given that solutions I've tried for similar problems are not working.

Problem

Given that you have this square:

.14   .21
.22
.17   .26


and this one:

.4    .3
.0
.2    .1


What should replace the question mark in this one:

.0008    .007
?
.06      .1


Working It Out

I was trying variants of multiply the bottom right/left and then the top right/left and then vice versa. None of those normal patterns seem to work, or I missed an obvious one.

I recognize that the first table is a 3-4-5 pattern but I don't know if that matters. (Meaning, .14 to .17 is 3; .17 to .21 is 4; .21 to .26 is 5.) But that doesn't hold for the other squares, even as a general pattern.

If anyone has any ideas, I'm open to them.

The middle term seems to be:

1 minus the sum of the other four terms

In the case of the first, this equates to:

$1 - (.14 + .17 + .21 + .26) = 1 - .78 = .22$

In the case of the second, this equates to:

$1 - (.4 + .3 + .2 + .1) = 1 - 1 = 0$

This leads us to our final result of:

$1 - (.1 + .06 + .007 + .0008) = 1 - .1678 = .8322$

• Thank you. I appreciate this explanation. And I'm sad that I didn't pick up on this myself. Aug 30, 2017 at 13:11

One solution is

bottom right plus bottom left minus top right. This would give 0.153 for the question mark.

It feels odd not to use the top left, but it works.

• You know it's interesting that this happens to work in this particular circumstance with the numbers as provided. Huh. Aug 30, 2017 at 13:11
• It is interesting. I am sure that if there was one more sample, my answer would break. Aug 30, 2017 at 18:04

It would appear that each of the puzzles

The first puzzle:

$0.14 + 0.17 + 0.21 + 0.26 + 0.22 = 1$

And the second puzzle:

$0.1 + 0.2 + 0.3 + 0.4 + 0.0 = 1$

Since the third puzzle is already:

$0.0008 + 0.06 + 0.007 + 0.1 = 0.1678$

That would make the solution:

$1 - 0.1678 = 0.8322$

I actually realised after joining that Green already posted this but explained differently.

• Thanks for the edit @Alpha, in my mind I meant to use spoiler blocks but clearly not.
– Tas
Aug 30, 2017 at 2:20
• Haha, all good. I'm still getting used to formatting here too. Aug 30, 2017 at 4:27