# What numbers do they mean?

There are four nations using different types of numbers in mathematics. There are:

Nation x: A, B, C, D

Nation y: 1, 2, 3, 4

Nation z: i, ii, iii, iv

Nation t: a, b, c, d

They may not be the same values when converting their numbers to another nation, e.g.: 1 may not equal to A or i or a.

You are given some clues:

1. The value of A in nation y is either 3 or 4 and in nation z is neither iii nor iv
2. The difference of D minus C in nation y is larger than 1 in our understanding
3. The value of B in nation z is not iv
4. The value of 2 is equal to d but not equal to ii
5. The value of i in nation t is c or d
6. The alphabet that comes before the value of B in nation t is equal to iv in nation z and 4 in nation y
• Hi QingHong, when you say "We are given some clues" this sounds like you found the puzzle elsewhere - if so, could you please include an attribution as to where you came across it, so that the original content creator gets credit? Thanks :)
– Stiv
Oct 9, 2020 at 8:47
• Ah okay, no worries - thanks for confirming :) Just wanted to check!
– Stiv
Oct 9, 2020 at 9:00
• The numbers mason, what do they mean? :) Oct 9, 2020 at 10:40
• I want to clarify for clue 2, is the number 1 referenced in the question our understanding of 1 (like, real world) or nation y's understanding where it could mean a different value? Oct 9, 2020 at 12:42
• Could we please convert nation y to the "opqr" number system? Having actual numbers floating around the puzzle only makes it harder to read, since you always have to check if it's nation y's system or ours.
– Bass
Oct 9, 2020 at 12:45

I think the solution is

A = 3 = ii = a
B = 2 = i = d
C = 1 = iii = b
D = 4 = iv = c

with the solution graph

• Any chance you could provide some selected logic steps, please? After applying all the base clues I ended up hitting a dead end with only clue 6 logic left in play and I still can't see where I went wrong - would be interested to find out...! Thanks :)
– Stiv
Oct 9, 2020 at 15:57
• @Stiv I can do so, but to be honest rot13(V tbg fghpx univat gb thrff N gb n naq P gb o (naq fb ba) nf V pbhyqa'g svther bhg sebz gur pyhrf. NSNVX gubfr frgf pna or fjvgpurq onfrq ba gur pyhrf tvira.) Oct 9, 2020 at 18:33
• Ah, that's what I feared, as I couldn't find a way to make the solution unique either... This was as far as I got, then I couldn't spot the next step. I'd be keen to know if anyone can point out my error!
– Stiv
Oct 9, 2020 at 19:12
• @Stiv rot13(Onfrq ba gur ynfg pyhr, jr xabj gurer vf n inyhr gung pbzrf orsber O, fb O pnaabg or gur ybjrfg inyhr. Gung zrnaf gung P vf (onfrq ba gur bgure vasbezngvba lbh unir va lbhe tencu) vf gur ybjrfg naq O vf gur frpbaq ybjrfg. Gung fubhyq trg lbh n ovg shegure.) Oct 13, 2020 at 17:37
• Hmmm... I thought I'd dealt with that already, since the lowest value in 't' is 'a', which I therefore ruled out. I think there must be an easier way to present this puzzle without causing so much confusion about values in all these different number systems...
– Stiv
Oct 13, 2020 at 17:43