In Germany, during World War 2, a new number system was designed. That number system had only 26 possible numbers (first 26 natural numbers) which were represented by alphabets A, B, C … X, Z (not necessarily in the same order as the 26 natural numbers) and the rules of multiplication, addition, subtraction, division held only if the result could be represented by one of the 26 numbers. In other words, if the product/ sum /quotient/ remainder was within the range [1, 26] only then the product/ sum /quotient/ remainder existed.
In that number system L, K, R, W, G, D, T, U, Y represent prime numbers & the following is known about them:
1) G is either the number which is at a distance of 10 from two primes or the number which has equal number of prime numbers lesser & greater than itself.
2) Product of G and D exists but product of G and U doesn’t exist.
3) X and U give the same remainders when divided by 10, and W > X.
4) G and W have a difference which is a perfect square of a prime number.
5) U can have a valid product with 3 of the prime numbers.
6) Absolute difference between the average of T and L, and Y is some number other than T, L and Y.
7) T has products with more numbers than Y.
Find which numbers are specifically represented by the alphabets - L, K, R, W, G, D, T, U, and Y
Provide the detailed solution and win reward points.
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