# A number association puzzle

These 0 to 10 digits are associated with the specific numbers as shown below.

What are the associated numbers for digits 9 and 10? Why?

Bonus: Is there an associated number for 11?

• Bonus: Yes, if you count spaces. Jun 20, 2022 at 1:01
• I'm assuming 11 is a big number? Jun 20, 2022 at 10:10
• @DanielMathias but then some of the numbers given no longer match up, so I'd think spaces are off limits, unless you are saying you count spaces, but not hyphens, in which case I'd have to check. Jun 20, 2022 at 12:55

First notice that the numbers on the right are

Divisible by the numbers on the left

and that

dividing by the number on the left (for 1 onwards) gives 4,3,11,9,6,9,8,5 which are the numbers of letters in the English spelling of the numbers on the right.

So we are looking for

Numbers such that when you divide the number by the number of letters in its English spelling it gives 9 (and 10). Given that we seem to be looking for the smallest such numbers I think the corresponding answers will be
9 -> 81
10 -> 50
I have yet to find one that works for 11 so not sure that it exists.

• Perfect logic. Well done. I would be interested in your quest for 11. I can tell you one for 12 exists. Jun 19, 2022 at 23:25
• I checked the first 25,000 or so multiples of eleven, didn't see any that matched, that high gets way off, so I don't think it exists for English unless you are willing to entertain alternate spellings (ninty-nine) go.dev/play/p/ZPR7NEXDI5k (I know my toText method could be better, but I wanted to output it in a quasi-legible way._ Jun 20, 2022 at 2:41

Played around a bit more. Here's an updated list that has numbers for 11 and a few more.

If you use the rule of using "and" for numbers greater than 100, you get the number for 11 (I've included a few more too) (88 of the numbers 1-100 have values with this, see https://go.dev/play/p/1gTZV38SapT)

• That is great @Jason. Thank tou. Jun 20, 2022 at 12:54