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More ways to get Braingle...

Rex and Ralph: Mystery Number

Math brain teasers require computations to solve.

 

Puzzle ID:#44017
Fun:*** (2.65)
Difficulty:**** (3.25)
Category:Math
Submitted By:javaguru*us**

 

 

 



Two mathematicians, Rex and Ralph, have an ongoing competition to stump each other. Ralph was impressed by the ingenuity of Rex's last attempt using clues involving prime numbers, but he thinks he's got an even better one for Rex. He tells Rex he's thinking of a 6-digit number.

"All of the digits are different. The digital sum matches the number formed by the last two digits in the number. The sum of the first two digits is the same as the sum of the last two digits."

"Take the sum of the number, the number rotated one to the left, the number rotated one to the right, the number with the first three and last three digits swapped, the number with the digit pairs rotated to the left, and the number with the digit pairs rotated to the right. The first and last digits of this sum match the last two digits of the number, in some order."

Ralph then asks, "If each of the three numbers formed by the digit pairs in the number is prime, then what is the number?"

Rex looks confused, and for a moment Ralph thinks he's finally gotten him. Then Rex smiles, scribbles a few things down on a pad of paper and then says, "Very nice, Ralph!"

Rex then tells Ralph his number.

What did Rex say?


(See the hint for an explanation of the terminology.)

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Comments

HellColdAeg*
Feb 05, 2009

Excellent one. Really great...
precious1026Aus*
Feb 07, 2009

Did your really think someone could follow that train of thought without a paycheck? I usually like all teasers, but this one was off the hook. But once I saw your train of thought and looked at the six digit number, which you led people to believe, the six digit number could have been any sic digits. I love Braingle. and you too. Good Teaser, boring but good, I hope you are truly good in math? You are not lying to us?
javaguru*us*
Feb 07, 2009

I think the train of thought in the teaser was easier to follow than your comment...did you have a point?
sfun3
Feb 08, 2009

loved this one as well! Excellent thinking!
ronhoward*
Feb 08, 2009

Wow. The train of thought ran right over me!

This seemed to be impossible at first, at least impossible to have a unique solution. It was amazing how as I worked on it the choices kept narrowing down. I thought this one was actually quite a bit easier than your Polygonal House teaser, probably because I got the "aha!" quicker on this one.

Another incredible teaser! Keep 'em coming!

How do you come up with these?
javaguru*us*
Feb 08, 2009

Thank you ron for the comment and complement!

When creating a teaser, first I try to find some interesting principle or quirk of math, probability or logic to exploit. Then I play around with different ideas using it until I find one I like. Then I try to (at least in the case of the Rex and Ralph teasers) determine what the minimum set of information will allow the solution to be determined. After I've worked out the math, at some point I get around to creating the teaser. I have about a dozen teasers right now where I've completed the math aspect, but just haven't had time to write a pleasing teaser around the math. In a few cases the teaser is written, but I haven't been able to simplify the explanation as much as I'd like.

I guess the main other "secret" to writing a good teaser is to be your own harshest critic. I discard most of my ideas and keep some around for a quite a while because they just don't feel right.

I know there's a large portion of the population on Braingle that won't ever appreciate my teasers because they require real effort, but I'm OK with that. I like them.
sfun3
Feb 09, 2009

Can't wait for the next one.
I can only really deeply appreciate all the thought going into those puzzles. I can solve them, but it is sooo much harder to come up with a good puzzle and construct an interesting story around it.
And don't worry about the community, there are enough of us loving these kind of puzzles.
shooter800*
Apr 28, 2009

great work , but that suppose to have one solution i think it have more than one lets see

145823

that number is prime and all of your conditions approved
shooter800*
Apr 28, 2009

sorry u wrote "If each of the three numbers formed by the digit pairs in the number is prime, then what is the number?"

but i read each ( any) great puzzle thank u
bigpatAus
May 08, 2009

Great puzzle. I solved the puzzle slightly differnetly than the given solution. I assumed (and wrongly) that zero wasn't one of the answers. Turns out I still got the right answer and after a little thinking I figured out that my method would have still eliminated zero so its all good
Lightspeed
May 08, 2009

I think this is the best puzzle where you have to figure out the number from clues about the digits. I love how at first it doesn't seem like there is enough information to arrive at a unique answer. I played around with the sum of the six numbers for a little bit before recognizing that each column in the sum contained the same set of digits. The Aha! moment was great!

Brilliant puzzle!
rlc327us*
Jul 19, 2010

I got 314113 (we'll call that number x)

digital sum (aka sum of digits or SOD) = last 2 digits : 13 = 13

SOD 1st 2 = SOD last 2 : 4 = 4

x rotated "a lot : 1444443

1st and last of "x rotated a lot" = last 2 digits of x : 13 = 13

Prime number digit pairs : 31, 41, and 13.
rlc327us*
Jul 19, 2010

continuation of above:
but the teaser was GREAT. i'd love to see more of these!
javaguru*us*
Jul 19, 2010

ric: Your answer doesn't meet the criteria "all digits are different".
eighsseAus*
Sep 24, 2013

This was an excellent one!

I seriously almost got it, but I came up with 430,217, and I thought I had it so I stopped looking. But I was overlooking that one little clue -- the sum of the first two digits is equal to the sum of the last two digits!



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