Yesterday I bought two tickets to a movie, which logically had consecutive numbers. I examined the numbers, which had four digits, and mentioned that the sum of the eight digits was 25.

A friend asked if any digit appeared more than twice out of the eight, and I answered him.

Other friend asked if the sum of the digits of either ticket was equal to 13, which I also answered.

And then, to my surprise, my daughter told me what the two numbers were!

What were they?

There is nothing in the problem that states that there CANNOT be any digit appearing more than twice, so the answer to the first question could be either yes or no. For example, the numbers 0444 and 0445.
The answer to the second question could also be either yes or no. It would be no for those numbers ending in 99 and 00. For all other possibilities it would be yes. What about all the numbers that do NOT end with 99 and 00.
Just for the numbers that start with 03 alone I came up with nine possibilities. They are 0318,0319; 0327,0328; 0336,0337; 0345,0346; 0354,0355; 0363,0364; 0372,0373; 0381,0382; 0390,0391.

Posted by James on 2005-11-23 00:25:25