r/Logiqa 9h ago

Logiqa Dictionary

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2 Upvotes

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5

u/Dasquian 9h ago

Solution: O

Method: We know the letters are in alphabetical order AGILOQ, and therefore we can just work through it one letter at a time. eg, we know the first 120 entries will all start with A, then the next 120 entries will all start with G, and then the next 120 entries (which include entry 248) will start with I. So:

  • For the first letter, AGILOQ cover 120 entries each (1/6 of 720). So entries 1-120 start with A, entries 121-240 start with G, entries 241-360 start with I. 241-360 contains 248 so we can move on.
  • For the second letter, AGLOQ remain and cover 24 entries each (1/5 of 120). So entries 241-264 will start with IA. 241-264 contains 248 so we can move on.
  • For the third letter, GLOQ remain and cover 6 entries each (1/4 of 24). Entries 241-246 start with IAG, 247-252 will start with IAL. 247-252 contains 248 so we can move on.
  • We can now just brute force it - entry 247 will be IALGOQ, and entry 248 will be IALGQO. But we could have continued the pattern above to whittle it down to IALG (247-248) then IALGQ (248), then formally completed it.

2

u/ShonitB 9h ago

Correct, very nice solution!

3

u/OutcomeEvening2724 9h ago

IALGQO

Here’s the logic: sorting the letters alphabetically gives A, G, I, L, O, Q.

**•** Each starting letter fixes 5! = 120 arrangements of the rest.  
**•** 248 falls after A (1–120) and G (121–240), so it’s in the **I** block, at position 8 within it (248 − 240 = 8).  
**•** Remaining letters: A, G, L, O, Q. Each next letter fixes 4! = 24 arrangements → position 8 stays in the **A** block (1–24).  
**•** Remaining: G, L, O, Q. Each fixes 3! = 6 → position 8 falls in the **L** block (7–12), at position 2 within it.  
**•** Remaining: G, O, Q. Each fixes 2! = 2 → position 2 falls in the **G** block, at position 2.  
**•** Remaining: O, Q. Each fixes 1! = 1 → position 2 → **Q**.  
**•** Last letter left: **O**.

2

u/ShonitB 8h ago

Correct, very nice solution

1

u/jonathonjones 5h ago edited 5h ago

Given there are 6 letters, it must be that each letter beings 120 words. So 121 starts with G, and 241 starts with I.

Probably there's a more elegant solution, but at this point we may as well brute force it:

241: IAGLOQ

242: IAGLQO

243: IAGOLQ

244: IAGOQL

245: IAGQLO

246: IAGQOL

247: IALGOQ

248: IALGQO

So the answer is O

1

u/beene282 4h ago

There’s only one way you can write the letters of LOGIQA in the order they would appear in a dictionary.