Each different capital letter below represents a different digit. Each occurrence of the same capital letter represents the same digit.

ZWEI is a prime number.
DREI is a triangular number (that is, of the form n*(n+1)/2)
VIER is a perfect square.

What do DREI and VIER represent?

Added logic bonus:

If I told you there were no zeros anywhere, and I also told you that giving you the value of Z would allow you to figure out what ZWEI represented, what would you say the value of ZWEI is?

Examining the four-digit triangular numbers with distinct digits (to include even those that have a leading zero, ie. 3-digit triangular numbers) and the four-digit perfect squares, I concluded that DREI is 1653 and VIER is 4356.  

The prime numbers of the form ZW53, where Z and W are distinct and not 1, 3, 4, 5, or 6 (to include those that have a leading zero) are: 0853, 0953, 2053, 2753, 2953, 7253, 7853, and 8753.  Two numbers of the list begin with 0, three numbers begin with 2, two numbers begin with 7 and only 1 begins with an 8.  As we are told that we can identify ZWEI with knowing the value of Z we can conclude that Z must be 8...hence ZWEI is 8753.

Posted by Dej Mar on 2007-06-24 06:48:58