Can My Selfie Fit This Huge Frame?
Windows are back!
Here I connect some windows (see this to know what it is) to form an image frame.
The frame has thickness, width and height of , respectively. Here's the model:
How many triangles are there in the frame?
Bonus: Generalise it for a frame of size .
The answer is 120876.
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1 solution
Count the triangles of a 1 by 2 0 1 6 chain: 2 0 . 2 0 1 6 − 1 0 = 4 0 3 1 0
Count the triangles of a 1 by 1 0 0 8 chain: 2 0 . 1 0 0 8 − 1 0 = 2 0 1 5 0
Sum up and minus the triangles of 4 windows in coner (they were counted twice each) : 2 . 4 0 3 1 0 + 2 . 2 0 1 5 0 − 4 . 1 2 = 1 2 0 8 7 2
Wait! We didn't count these 4 triangles:
The answer is 1 2 0 8 7 2 + 4 = 1 2 0 8 7 6
P/s: Yes, you can. Take a selfie :)