Problema Solution
Taha received his locker combination for his new locker. He noticed that each of the three integers of the combination is a prime, the sum of 3 integers is 50, and the three integers are in decreasing order. What is the value of the last digit of Taha's locker?
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let x, y and z be the three prime integers and x>=y>=z
the sum of 3 integers is 50:
x + y + z = 50
z + z + z <= x + y + z = 50
3z <= 50
3z <= 50/3
z < 17
if z is odd integer then 50 - z is also an odd integer which is in contradiction with the fact that the sum of the 2 other prime integers must be a prime number. Thus we conclude that z is even prime number that is z = 2.
the value of the last digit of Taha's locker is 2.
let x, y and z be the three prime integers and x>=y>=z
the sum of 3 integers is 50:
x + y + z = 50
z + z + z <= x + y + z = 50
3z <= 50
3z <= 50/3
z < 17
if z is odd integer then 50 - z is also an odd integer which is in contradiction with the fact that the sum of any 2 other prime integers that are not 2, must be an even number.
Thus we conclude that z is even prime number that is z = 2.
the value of the last digit of Taha's locker is 2.