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Quite a coincidence (Posted on 2018-01-19) Difficulty: 2 of 5
"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.

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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