# A puzzle with grids and lines

What would be an appropriate song to listen to after solving this puzzle?

EDIT 1 [June 14, 2022]

• Fixed the two top left grids being coloured incorrectly
• Fixed one of the 6 missing a connection
• The operator labelled 6 on the right has 2 inputs whereas the one on the left has at most 1 input. Is this correct? Commented Jun 13, 2022 at 18:44
• No, of course not. That has been fixed. Commented Jun 14, 2022 at 11:20
• The row of not equals statements linked together at the bottom is not intended to mean that none of them are equal, right? I.e. 2 cannot equal 1 or 3, but could equal one or more others as long as the entire statement is true, such as 4 and 6.
– JLee
Commented Jun 14, 2022 at 15:51
• @JLee Yes, all 7 diamonds are distinct. Commented Jun 15, 2022 at 9:44
• Please double-check the grid at the bottom under the 7. I think rows 3 and 4 should be all red instead of all white.
– JLee
Commented Jun 15, 2022 at 16:07

Just continuing on from SQLnoob's answer since they're incredibly close,

the images spell out "JSaBLv4" short for Just shapes and beats lvl 4, which is titled LOGIC GATEKEEPER

The black diamonds appear to be Boolean operations that act on the grids. We are given that 1 is NOT (which solves F), 6 is NOR, and 7 is XOR. Since C has no arrows pointing into it, 3 must be reversible, and if all 7 diamonds represent distinct operations then 3 must be XNOR.

This allows us to solve D, B, C, and G in one fell swoop, and also show that 5 is NAND.

Here's where everything falls apart:

Look at the top 4 and the 2, and consider the function (x4y)2z. If 2 and 4 are both functions like 1, 3, 5, 6, and 7, then this composition is also a function. However, the third and fifth rows of the second column have identical input triplets (011) and opposite outputs, and broadening our possible scope of functions (for example, allowing 4 to flip its left input vertically and its right output horizontally, which is the only way to introduce flips to 4 so all of this checks out) destroys our ability to do deductions.

• Yep, I've made a mistake in labeling some of the grids at the top. The image has now been updated. Although, from your image, I can also see discrepensies that is not caused by the incorrect grids as well. Commented Jun 14, 2022 at 11:21

The seven black diamonds are

logic gates, as follows:

1 = NOT
2 = OR
3 = XOR
4 = AND
5 = NOR
6 = NAND
7 = XNOR

When applied to the images,

treating a white square as 1 and a red square as 0, we get the following for the missing images A-G: which appears to spell out JSoBLv4 (?).

But I don't know what song that is referring to.

• Strange how only 1 of the 7 logic gates match mine but answer is the exact same except for c
– JLee
Commented Jun 15, 2022 at 17:34
• Interesting, what do you have for C? Because that's the only one that isn't obvious (to me) what it's supposed to represent. Commented Jun 15, 2022 at 17:41