8
$\begingroup$

Bob: I hear you won the lottery.

Alice: So I did!

Bob: What six numbers did you win it with?

Alice: Can't remember. All I recall is that they were all different, and none greater than 28.

Bob: Anything else?

Alice: Yes. I checked that no other six different numbers, none greater than 28, have the same common factor graph as mine.

(The common factor graph of a set of integers is the graph whose vertices are the integers, two of which are joined by an edge if they have a common factor greater than 1.)

What six numbers did Alice win the lottery with?

$\endgroup$
3
$\begingroup$

Unproven Answer (I need to go out soon):

This is the graph:

enter image description here

And the solution is unique, which is:

$10, 14, 15, 20, 21, 28$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.