# Step into the Octagram

The diagram below shows a partially-filled "octagram". Step into it, if you dare!

At every vertex in a long word.
Flowing into every vertex are two short words. Anagrammed together, these two short words yield the long word.
Flowing out of every vertex are two more short words. Anagrammed together, these two short words also yield the long word.

For example, if the vertex word is BOOKCASE, then OBOE and SACK would be a legitimate pair of inflows (noting that OBOE and SACK anagrammed together yield BOOKCASE). The outflows could also be OBOE and SACK, or even SACK and OBOE. Or, the outflows might be some new pair, such as COOK and BASE (which anagrammed together also yield BOOKCASE).

Your job is to fill in the inflows and outflows (i.e., label the arrows). Also, for an extra challenge, I left one of the vertex words blank for you to figure out.

The missing vertex word is guaranteed to be unique from all the other vertex words. However, the short words might not be unique. You might see some short words reused as you go around the octagram.

Americans are asked to be forgiving of the British spelling of COLONISATION. Be assured that exotic spellings are not an issue with any of the short words.

Ready for another one? See if you can solve the heptagram.

• Is it allowed to use the same short word twice? – Rand al'Thor Jun 25 '19 at 15:15
• The example of BOOKCASE seems to indicate that is acceptable @Randal'Thor – LeppyR64 Jun 25 '19 at 15:32
• @Rand al'Thor — Yes, the short words may be reused as you go around the octagram. (Although the vertex words are all unique.) – SlowMagic Jun 25 '19 at 15:41
• This puzzle was so fun that I worked it to completion even after I saw that Rand had answered. I'd love to do another sometime! – TwoBitOperation Jun 25 '19 at 17:04
• Really neat idea for a puzzle. And it also "looks good" when presented. +1 from me – BmyGuest Jun 26 '19 at 13:18

Completed octogram and the word at the bottom:

DENOMINATORS

(I know you gave us an answer template, but I like the pictorial format!)

Solution process

The puzzle is actually in two halves (plus finding the bottom word), and each half is easy to complete once you find the first short word in it. Given one short word, say from long word A to long word B, you can easily get the other short word flowing into B and the other one flowing out from A, and just keep going both ways until you get a full chain connecting up at the bottom word. But that only solves half of the short words, and you still need to crack the separate chain containing the other half.

My original starting point was to try NATION (which quickly failed) or NOTION flowing between CONDENSATION and COLONISATION. That got me as far as this before I started hitting things that aren't words:

CONDENSATION
DANCES NOTION
PREDICAMENTS
DANCES PERMIT
SEMITROPICAL
PERMIT SOCIAL
DECLARATIONS
SOCIAL RANTED

COLONISATION
NOTION SOCIAL
REPLICATIONS
SOCIAL PINTER
PREMONITIONS
PINTER MONIOS

Then I gave up trying to "just spot" a linking short word, and applied some logic to the fairly dissimilar words CONDENSATION and PREMONITIONS. The letters CDAN and PMRI respectively are not shared, so the short word linking these two must be chosen from the letters ETONSION. Having excluded DANCES because I'd tried that word before, I went for putting ET with CDAN and PMRI and using ONIONS as the link. That educated guess was enough to solve the first half and the bottom word.

• NATION -> NOTION -> ONIONS was the exact route I took to start solving, which I find interesting. Great (and fast) solve! – TwoBitOperation Jun 25 '19 at 17:03

I'm slower than Rand, but I worked the other way so have the other half!

• Some of these are a bit hard to read. If you could replace them with text or write very neatly, that'd be fantastic. – RShields Jun 25 '19 at 15:39
• Nice! It's not immediately obvious that the puzzle is in "two halves", but indeed they're quite separate and we solved one half each :-) – Rand al'Thor Jun 25 '19 at 16:00