# Unravelling the Mystery of Clever Joe's Ticket Numbers!

• godchuanz
In summary, the conversation involved the speaker buying two movie tickets, bumping into a friend named Clever Joe, and playing a game where Joe had to guess the ticket numbers based on the sum of their digits and if any digit added up to 13. The correct answer was 1299 and 1300.

#### godchuanz

I wanted to catch the latest action show with my girlfriend, so I went to buy 2 movie tickets. Walking away from the counter, I bumped into a friend Clever Joe.

Clever Joe was interested to know my movie ticket numbers, but I cheekily refused to tell him the answer directly, telling him instead, "Each ticket number is 4-digit, and the sum of the 8 digits (of 2 tickets) is 25."

Clever Joe thought a little, and asked, "Does any ticket has its 4 digits adding up to 13?" I answered him (yes or no).

Clever Joe asked again, "Are you able to identify a single digit that appears the most times?" I answered him (yes or no).

To my surprise, Joe confidently and accurately told me what my 2 ticket numbers are.

The big question: What are the ticket numbers?

in white: ( tickets 1299 and 1300 )

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My (sort of) explanation:

Since they were bought at the same time, it's resonable to assume the numbers are consecutive. Most of the time, one would add up to 13 and one to 12. The only way it won't is for:

0399 0400
1299 1300
2199 2200
3099 3100

If the answer to the one adds up to 13 was yes, there would be no way to identify a single one from if it had a digit more common. 9300,9301 and 9210,9211 does, for instance, while 0138,0139 and 0147,0148 doesn't. Hence the first answer must be no. If the second answer is yes, there are three options, hence again no unique ID. If it's no, however, 1299,1300 is the only option. Since he did narrow it down, that must be the answer.

How did I get the existence examples and narrowing down? Exhausive search <hangs head in shame>. I'm sure there's an exceedingly clever way to do it without that, but I only have a couple of minutes before I have to go and while nothing is obvious to me, I can do a search in that :-). I'm sure Cleaver Joe must have done it some other way, but that's his headache..

[EDIT] Hey, wait a cotton pickin minute! Some of my answers do add up to 13! Man, this answer is totally whacko <tries to whipe some of the egg off his face>. Sorry 'bout that.. My explanation makes no sense at all and I'm an idiot for missing it. I'll leave it since I did say it, but I realize it's wrong.

[EDIT] Ok, so I now realize that I'm wrong in my edit and actually stand by my explanation and, while still an idiot, am now an idiot for thinking I was wrong. Yeah, that's a logic problem in itself. What happens when you don't take the time to think your thoughts through and rush off instead..

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in a simple way i can say that they were 4440,4441.
4 is repeated several times.
first one is 12 and second one is 13.

abinash said:
in a simple way i can say that they were 4440,4441.
4 is repeated several times.
first one is 12 and second one is 13.

Won't work. If the answers were Yes and Yes (respecivly) then Joe couldn't have uniquely identified the numbers and answered the question. 3630 3631, for instance, also add up to 12 and 13 and have a repeating digit, so there would be no way to tell if it'd be that or your answer (there are obviously a ton of others, I merely picked an existence example at random). The answers must have been something else in order for Joe to confidently give the correct answer (hint hint).

i guess that the numbers are 3333 and 3334.

if he say to first one then the sum of the numbers adds up to be 25.

and if he yes to second question then my second number adds up to be 13

agopikrishna16 said:
i guess that the numbers are 3333 and 3334.

if he say to first one then the sum of the numbers adds up to be 25.

and if he yes to second question then my second number adds up to be 13

Joe could CONFIDENTLY give me the ticket numbers, so he must have eliminated all other possibilities based on my 2 answers. If I had answered yes to both questions, there would be too many possibilities. So... wrong answer :)