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 Quite a coincidence (Posted on 2018-01-19)
"It's unbelievable!" exclaimed Jerry facing his three friends Adam, Dan and Betty.
"I've asked you to tell me independently each a 4-digit number and after a while, I'm happy to announce that if any of you will divide their number by mine you will end up with the same remainder! "
Now that you know it I'm sure that you will be able jointly to figure the value of my number...- of course it will be the largest of the qualifying candidate answers...

Adam: It could not be true for any three non-related 4-digit numbers!
Betty: You were extremely lucky to find such a special number!
Dan: And now we will be able to calculate the value of your number!

Indeed, Adam(2479), Betty(6181), and Dan(8649), after a not-so-long brainstorming session successfully restored Jerry's number.

a. What was it?
b. d4 bonus question:
What's the probability of Jerry "success" with 3 RANDOMLY CHOSEN
three 4-digits numbers.

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: proposed solution Comment 6 of 6 |
(In reply to proposed solution by Charlie)

Charlie is wrong in one small respect.  If two of the three numbers match, then Jerry's number is the difference between the distinct numbers, not their GCD.

For instance, if the numbers are 2000, 2000, and 9000, then the GCD is only 1000 but Jerry's number is the largest factor of 9000 - 2000, which is 7000.   This leaves a common remainder equal to the smaller distinct number, in this case 2000.

 Posted by Steve Herman on 2018-01-19 19:59:20

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