Ah, Hept-$. That’s got to be 7 as in heptagon. Turns out that was all I needed!

I got the same answers as ano above so I think I am correct. I also had no recollection that -ines did not exist, (absence of evidence not being…etc.) and the problem worked out okay.

Hurrah! I did so poorly at my first problem on here, I am relieved.

Thanks for sharing Tanya – a cool propblem indeed!

]]>Seems I consulted a wrong website for spelling of chemical names. “ine” should be replaced with “yne”. The problem works anyway. Also, “chemical elements” was a direct translation for Russian.

]]>I approached it similarly…but just remembered C2H6 = ethane from chemistry days….so thought C2H2 must be ethine…although I am pretty sure (now googled it!) there is no such thing as ethine…so well that was my cheat! ]]>

We can classify the names as follows:

* -ine versus -ene versus -ane: {Butine, Ethine, Propine}, {Heptene, Butene}, {Propane} (sizes 3, 2, 1)

* Prefixes: {Butine, Butene}, {Propane, Propine}, {Heptene}, {Ethine} (sizes 2, 2, 1, 1)

We can classify the formulae as follows:

* Number of Cs: {C3H8, C3H4}, {C4H6, C4H8}, {C7H14}, {C2H2} (sizes 2, 2, 1, 1)

* Number of Hs: {C3H8, C4H8}, {C4H6}, {C3H4}, {C7H14}, {C2H2} (sizes 2, 1, 1, 1, 1). Er, does not correspond to anything, so we’re stuck here.

Ok, let’s cheat and resort to using linguistic knowledge (it’s a linguistic olympiad anyway), namely that “heptene” suggests something to do with the number 7. So by making the guess (based on sizes) that prefixes correspond to number of Cs, we get:

Heptene = C7H14

Ethine = C2H2

{{Butine,Butene},{Propane,Propine}} = {{C3H8,C3H4},{C4H6,C4H8}}.

We need to figure out what the suffixes stand for. The *number* of Hs hasn’t been useful, so let’s try *ratios*. For “Heptene” with an “-ene”, the ratio of Hs to Cs is 2. Among the undetermined ones, there’s only one “-ene” (Butene) and only one with a ratio of 2 (namely C4H8), so let’s map them:

Butene = C4H8

Butine = C4H6

{Propane, Propine} = {C3H8,C3H4}

Since the number of Hs is always even, we should probably look at *half* the number of Hs. And since the number by itself wasn’t useful, let’s compare half the number of Hs to the number of Cs:

Heptene = C7H14 (7,7)

Butene = C4H8 (4,4)

Ethine = C2H2 (2,1)

Butine = C4H6 (4,3)

{Propine, Propine} = {C3H8 (3,4), C3H4 (3,2)}

Since both -ine’s we know have the second coordinate as one less than the first (and there’s exactly one unknown -ine name and exactly one such unknown formula), that’s probably what *-ine* means.

Propine = C3H4 (3,2)

Propane = C3H8 (3,4) So -ane means #H/2 = #C + 1.

Summarizing our knowledge so far:

Prefixes:

Hept: #C = 7

But: #C = 4

Eth: #C = 2

Prop: #C = 3

Suffixes:

ene: #H/2 = #C

ine: #H/2 = #C – 1

ane: #H/2 = #C + 1.

Cool. So C2H4 (2,2) = Ethene, C2H6 (2,3) = Ethane, C7H12 (7,6) = Heptine, Propane = (3,4) C3H8, Butane = (4,5) C4H10.

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