# The two combined

The answer is 14 letters in total. Good luck!

SQUARE-TRIANGLE

As solved by cap and Rand al'Thor,

The first step is the rebus:
We have the atomic number of Gallium 31 (although I'm more familiar with the atomic number being written in the lower left and mass number in the upper left)
Picture of THOR
Electron symbolizing negative charge, or in this case subtraction -
Hydrogen, i.e., H
All of this in the mirror gives ROT13

So, using ROT13 for the 5x3 rectangle of letters, we have

?BEEE
TSIRA
HAAHG

Now, the first picture also has a 5x3 rectangle of grids, where the shaded cells for all the grids combined form a triangle. Putting the letters from the last step in the corresponding positions in the triangle, we get this

    B
R A
A E S
T ? A E
H G I E H

From the above triangle, moving spirally, we can read
BASE, HEIGHT, AREA?

The third picture also tells us that all of the letters have a unit area and that we should try to find the smallest triangle where we can fit this triangle of letter squares. An isosceles triangle with base 6 and height 6 will obviously do the trick and also has the minimum area of any triangle covering the letters. The answers are then
Base=SIX, height=SIX, area=EIGHTEEN

Finally, finding these letters from the small letters of the 4x4 letter squares and picking the corresponding big letters, we get
six->SQU, six->ARE, eighteen->TRIANGLE.

SQUARE-TRIANGLE,
since we have a triangle made out of squares covered by yet another triangle!

• Everything as intended, well done! Nov 25, 2021 at 15:11

Firstly, the rebus in the second row:

69.72 is the atomic mass of GALLIUM, that's a picture of THOR and then an ELECTRON (negative charge), then 1.008 is the atomic mass and 1 the atomic number of HYDROGEN. So we get ... 31THOR-H. Put that in a mirror and it becomes ROT-13 (after removing the H from THOR).

Thanks to @cap for the correct symbolic interpretation of the first and third symbols.

Now, the first and third rows:

The highlighted cells in the rectangles in the first row show the positions into which we should place the letters from the box in the third row to form a triangle:

 O
 E N
 N R F
 G ? N R
U T V R U
After using ROT-13 from the previous row, this becomes:
 B
 R A
 A E S
 T ? A E
H G I E H

(Note to self: when N and R are the most common letters appearing in stuff, maybe ROT-13 is involved somewhere.)

Going around the triangle in a spiral starting from the top, we get BASE, HEIGHT, AREA, ?

However, I'm not sure where to go from here. Something about "minimum" needs to be used for this triangle, and presumably the number "1" from the left also needs to be used. Then we need to figure out how to apply it to the fourth row to get the final answer.

The fourth row contains three 4x4 squares of letters, in which each cell contains two letters, one big and one small. I'm wondering if we should extract some meaning for the base, height, and area of each of these squares, and also if the spiral pattern for the triangle is significant too - maybe we should be reading the squares in a spiral pattern?

For what it's worth, ROT-13ing all the big letters in the fourth row gives:

N Z V Y W U O R - Z C B N
M F O R T F G O - T E W G
S B E D R B N X - S H V U
H C Y S E Z H Y - Y J R A

• Hopefully this isn't considered too partial. I think the triangle thing is some decent progress, and I've probably exhausted all the information from the first two rows, so all that's left to figure out is how to complete the third row and then how to use that to get the final answer from the fourth row. Nov 23, 2021 at 7:10
• Nice, I found that same triangle but was hesitant to post a partial. Now we can work on it together. On the rebus rot13(abgvpr gur erq nern bs gur ryrzrag. V guvax vg jnagf gur ngbzvp ahzore sbe Tnyyvhz juvpu vf 31. Gur ryrpgeba vf artngvir be n zvahf fvta. 31GUBE - U = 31GBE naq chggvat gung va gur zveebe trgf EBG13. Gura gur yrggref bs gur gevnatyr fcryy ONFR URVTUG NERN?) I don't know what know what 'minimum' means or the 1 to the left of the letters. Nov 23, 2021 at 8:11
• @cap Oh, awesome find! Do you want to post another partial answer? Then we can both continue updating our answers and see who gets the prize :-P Nov 23, 2021 at 8:22
• @Randal'Thor, just after your recent comment now, I feel like I have to get it before both of you. Nov 23, 2021 at 8:29
• Good work, +1. I was about to steer you in the right direction for the rebus but cap's answer is correct ofc. Now, it's a matter of trying to make sense of the rest (the "1" and "minimum") Nov 23, 2021 at 8:42