# Devil goes Pan Digital..Sometimes Lucky..Sometimes not..Figure him out

$$Given$$:

D, E, V, I, L, G, N, O, T are distinct digits (1 to 9).

$$D+E$$ brings good luck

$$I+L$$ is unlucky

$$N+O-T$$ is unlucky too.

$$DDDD$$ = $$(D+E)^V$$ + $$(I+L)^G$$ + $$(N+O)^T$$

Fully Figure out this unusual unique devil.both Rep Digit and Pan Digital.

• whether a number is lucky and unlucky varies greatly in cultures... is this too broad? – Omega Krypton Jun 1 '19 at 11:20
• True..for puzzles sake...think them as clues ..leading to what if scenarios..leading to restricted choices for the digits..ultimately to final resolution – Uvc Jun 1 '19 at 13:19

$$6666 = (6+1)^4 + 13^2 + 16^3$$, with $$I,L$$ and $$N,O$$ being indeterminate.
$$D+E=7, I+L=13, N+O-T=13$$. We know $$I,L,N,O,T,V,G\gt1$$, so $$D$$ or $$E$$ equals $$1$$. (and $$6666$$ looks like the obvious choice!). $$V,G,T\in\{2,3,4\}$$ as $$7^5\gt6666$$. $$N+O\gt14$$ (as $$T\gt1$$), and considering $$15^2, 16^3$$ ($$17^4$$ is way too big), and noting that $$13^4\gt6666$$ gives only two options, leaving $$7^4=2401$$ as the first addend, and $$D=6$$.