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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
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1 Answer 1

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30
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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 -> H818
273 -> F318
183 -> A318
290 -> G218
205 -> B718
294 -> G618
220 -> C418
308 -> H218
242 -> D818
199 -> B118

And for not chess numbers:

315 -> H918
372 -> 12C18
180 -> A018
284 -> FE18
208 -> BA18
300 -> GC18
320 -> HE18
208 -> BA18
225 -> C918
198 -> B018

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4
  • 2
    $\begingroup$ Wonderful job! : ) $\endgroup$
    – PiGuy314
    Dec 8, 2021 at 16:47
  • 2
    $\begingroup$ Expecting Go Number™. $\endgroup$
    – WhatsUp
    Dec 9, 2021 at 21:10
  • $\begingroup$ @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? $\endgroup$
    – Stef
    Dec 17, 2021 at 8:27
  • $\begingroup$ @Stef Well, something like that (: $\endgroup$
    – WhatsUp
    Dec 17, 2021 at 8:54

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