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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.)
 Part A only | Comment 1 of 6
The pair-wise differences should help
6181-2479=3702
8649-2479=6170
8649-6181=2468
Hmm that last one is interesting but I don't see a pattern.  Let's do it again
6170-3702=2468
6170-2468=3702
3702-2468=1234
Ah, a pattern.  Multiples of 1234.  I wonder if that's the number.
2479/1234 = 2 remainder 11
6181/1234 = 5 remainder 11
8649/1234 = 7 remainder 11

Jerry's number is 1234.

 Posted by Jer on 2018-01-19 07:39:52

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