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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.
Provide your estimate, listing your assumptions and reasoning.

 No Solution Yet Submitted by Ady TZIDON Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Part A only | Comment 2 of 6 |
(In reply to Part A only by Jer)

Only two pairwise differences are required.

6181-2479=3702
8649-6181=2468

Jerry's number must be the GCD (Greatest Common Divisor) of these two numbers.

It must also divide the difference, so it must divide
3702-2468 = 1234.

and 2468 - 1234 = 1234, so the GCD is 1234

 Posted by Steve Herman on 2018-01-19 09:47:52
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