# What is a Chess Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.

If a number conforms to a special rule, I call it a Chess Number™.
Use the following examples below to find the rule.

Chess Numbers™ Not Chess Numbers™
314 315
273 372
183 180
290 284
205 208
294 300
220 320
308 208
242 225
199 198

For easier analysis, here is a CSV version:

Chess Numbers™,Not Chess Numbers™
314,315
273,372
183,180
290,284
205,208
294,300
220,320
308,208
242,225
199,198


A Chess Number™ is a number that

when converted to base 18, results in a valid coordinate pair for a square on a chess board (everything between a1 and h8).
Base 18 is chosen because it is the lowest base which has an h as a digit.

Here are the results for chess numbers:

314 -> H818273 -> F318183 -> A318290 -> G218205 -> B718294 -> G618220 -> C418308 -> H218242 -> D818199 -> B118

And for not chess numbers:

315 -> H918372 -> 12C18180 -> A018284 -> FE18208 -> BA18300 -> GC18320 -> HE18208 -> BA18225 -> C918198 -> B018

• Wonderful job! : ) Commented Dec 8, 2021 at 16:47
• Expecting Go Number™. Commented Dec 9, 2021 at 21:10
• @WhatsUp When converted to base-30, it looks like letter-digit or letter-digit-digit, with the digit part forming a number between 1 and 19, and the letter not being an i?
– Stef
Commented Dec 17, 2021 at 8:27
• @Stef Well, something like that (: Commented Dec 17, 2021 at 8:54