# What is an Indivisible Word™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.

If a word conforms to a special rule, I call it an Indivisible Word™.

Use the following examples below to find the rule.

Here is a CSV version:

Indivisible Word™,Not Indivisible Word™
ACE,PRO
ICONS,SYMBOLS
DRY,WET
TENURE,FIRED
VASE,PITCHER
TAME,WILD
DEBASE,REBASE


These are not the only examples of Indivisible Word™ (or Not Indivisible Word™), more can be found.

Hint 1:

Levieux has already pointed out atoms as "indivisible," but what are other things that might be described as indivisible? Concepts, words, numbers, nations, people?

Hint 2:
A Limerick

A dozen, a gross, and a score
All times the third power of four
Take from that eleven
Times seventy seven
Then from that four-twenty-two more

• What approach do you recommend for solving this? Commented Feb 6, 2018 at 18:53
• @Guest The first link in the puzzle will take you to results for a search that has several similar puzzles. The name for the word type is a hint as to what makes a word qualify, but I won't be giving any other hints until some time tomorrow at the earliest. Commented Feb 6, 2018 at 19:04
• Thanks. I'm not really looking for hints, just asking what kind of approach we should be taking in general. As in, it doesn't seem like a deductive or analytical approach is really possible, so I'm wondering if we're basically just supposed to try stuff at random and see if things happen to work out (not sure if there's a name for that kind of approach). Commented Feb 6, 2018 at 19:08
• To start, you'll basically need to make guesses and test them. You can look at similarities between the words that match, or differences between them and the words that are on the other side. You'll note that, on each row, the words tend to be related somehow, which can help narrow things down, For example, "debase" is paired with "rebase," which shows that the rule isn't directly related to the root "base". Commented Feb 6, 2018 at 19:15
• Hmm, the name "indivisible" immediately made me think of atoms/atomic and therefore of chemical elements. And although most not indivisible words can be "split up" in elements (e.g. Pr-O, H-At-Es, Re-Ba-Se) and most indivisible words cannot, there are exceptions on both sides (e.g. Te-N-U-Re). Commented Feb 7, 2018 at 10:00

Indivisible Words when converted to numbers using ISO 9995-8 (phone keypad) are prime numbers

Indivisible words:

I will leave it to the reader to verify that they are all prime:
ACE = 223
ICONS = 42667
DRY = 379
TENURE = 836873
VASE = 8273
TAME = 8263
DEBASE = 332273

Non-indivisible (sometimes known as "Divisible") words:

PRO = 776 (2 x 2 x 2 x 97)
SYMBOLS = 7962657 (3 x 401 x 6619)
WET = 938 (2 x 7 x 67)
FIRED = 34733 (47 x 739)
PITCHER = 7482437 (1447 x 5171)
WILD = 9453 (3 x 23 x 137)
HATES = 42837 (3 x 109 x 131)
REBASE = 732273 (3 x 244091)
MEDAL = 63325 (5 x 5 x 17 x 149)
GAL = 425 (5 x 5 x 17)

Hint #2 explained:

((12 + 144 + 20) x (4^3)) - (11 x 77) - 422 = 9995

• I knew it was something to do with primes, I just couldn't work out what. Nicely worked out! +1 Commented Feb 8, 2018 at 22:04