A set of five dice is marked 1 to 6, but instead of commonly used spots bears Arabic digits .
After a single roll of dice they are arranged to represent a 5-digit number.
It is found that this number fullfils ALL of the following conditions:
1. There is no descending order of digits within this number.
2. No digit is repeated more than twice within this number.
3. At least one of the digits in the number is bigger than 5.

How many such 5 - digit numbers exist?

(In reply to computer findings--unambiguously by Charlie)

 

Charlie,

75 is definitely the correct answer for the dot-marked dice, where no ambiguity exists regarding the interpretation of  the number of dots.

 On the other hand  whoever got ,say 1;3;5 and two sixes(NORMAL DIGITS) and wrote down 13566, could arrange the dice as

 13569 or 13599 and still comply with the 3 conditions mentioned in the problem.

Therefore the correct answer for the case of the ambiguous dice is significantly higher than twice 75 and I  leave it to you to provide it , if you are so inclined.

Clearly, your new list will start with 56699 and terminate by 11226.

 

Significantly bigger challenge is solving the problem with P&P.

Everybody is welcome.

Posted by Ady TZIDON on 2010-12-22 17:42:14