Puzzle_5

1. what is the 5 digit number which has only 2 prime numbers in it and satisfies the followingcondition.
a. 3rd digit is the largest
b. 2nd digit is the smallest
c. 1st digit is one less than the 3rd digit and greater than theaddition of 4th and 5th digit.
d. 5th digit is between the 1st and 2nd digit and half of the 4th digit.
1 is not considered as the prime number

Solution:
2nd digit is the smallestso it must be 1.
3rd digit is the largest
so it can be 9 and the first digit is 8.
1st digit is greater than theaddition of 4th and 5th digit.
so it can be 1,2;2,1;3,4;4,3;2,3;3,2;2,4;4,2 but 5th digit is between the 1st and 2nd digit and half of the 4th digit
so it can be 4 and 2 and so we should have 1 more prime no.
so the third digit cannot be 9 it should be 8 and the first digit is 7.
so the number is 71842

2. (Most Difficult one) What is the value of X,Y and Z?
X X X X
Y Y Y Y
Z Z Z Z
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Y X X X Z
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Solution: Well, to get X+Y+Z = Z, we should have X and Y as O which is not possible, So if we take X and Y such that X + Y = 10, we can get X + Y + Z = Z, carry 1.

At the next stage, we should get (carry)1+X+Y+Z = X, so we have to choose Y and Z such that Y + Z = 9. So, 1+X+Y+Z = X, carry 1.

At the next stage also, 1+X+Y+Z = X, carry 1.
At the final stage we have to get, 1+X+Y+Z = YX. Since, 1+X+Y+Z gives the value X and carry 1 we get the value fo Y as 1.