perplexus.info :: Just Math : Quite a coincidence

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.)

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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