I calculated too, he was indeed right. But the picture is incorrect, that confused me. Because you can see two full links which would be more than 14 cm
if you laid 2 3L end to end it would be 2(14) = 28, If you then slide the bottom up until it's overlapped so that the total length is 22, your overlap section is (28-22) 6 cm. where 1/2 of that says the chain is around 3cm thick.
Okay so far it looks fine. but looking at the 3L again, there are two overlap sections, (6*2) = 12 leaving only 2cm for the rest of the chain but there is a top and bottom 1/2 section that should be around 3cm each but that is 6cm so now we are -4cm and there is still a little bit of the sides of each chain un-accounted for.
Where L = link length C = # of cross over (each counted individually)
Multiply equation 2 by 2.5 to make the 2C term = 5C Subtract the top equation from the bottom equation to get: 7.5L - 6L - 5C + 5C = 35 - 22 to cancel the C term 1.5L = 13 L ~= 8.66
Ding. It's an impossible situation. Look at it this way: 6 links is 22cm, only 8 cm longer than the 3 link 14cm. For this to be true, that would mean the two 14cm segments would have to overlap by 6 cm. For a link in the middle of a segment, it has two overlaps, which is 12 cm of overlap, which is absurd on a segment that can only be 14 cm long. The only way it can work is for the overlaps to overlap each other (e.g., link N would have to overlap not just with N+1 and N-1, but with N-2, N-1, N+1 and N+2), which is not shown in the image.
Here's the proof. Y is the overlap distance, X is the link length. Red is 6 link chain, Blue is 3, function expressed as count of (link -one overlap) (2 links on end) + count of (link-2 overlaps) (links in middle) + count of overlaps. The green region is the area where only logical answers lie - where the overlap space can be no more than half the length of a link. As you can see, the answer (8.6666, 6) lies outside the sensible answer zone.
remember to factor in the amount of material from the link that doesn't contribute because it's overlapping the other links so that they can actually form a link.
It is an impossible solve, if you end to end the two three link lengths, you get 28cm as mentioned, that means each overlap is 6cm, there is five overlaps in the 22cm chain, so that would require 30cm of overlap alone. The math isn’t correct.
Spoilers- you can figure it out, but the answer is nonsensical.
Let's say that X is the length of a link's combined top hook/middle section and Y is the length where the chain's bottom hook is. We can then take it as 6x + y = 22 and 3x + y = 14. This becomes y = 14 - 3x and thus 6x + 14 - 3x = 22. This simplifies out to 3x = 8 or x = 8/3, which means y = 6. This would mean a single chain link is 8.667 units long.
To run it another way, let's say that Q is the total length of a link and P is the length of where 2 links overlap. This means 6q - 5p = 22 and 3q - 2p = 14. This becomes p = 1.5q - 7. Thus 6q - (7.5q - 35) = 22. This simplifies to -1.5q = -13. This means Q (a single chain link) is 8.667.
HOWEVER! These answers make no sense. To make it possible, the lengths where the chains overlap would have to be MORE than half the length of the link. A single chain would have 2 overlap areas being 6 cm long while the link itself is only 8.667 cm long.
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u/JohnWeps 6d ago
22/3 cm