Marvin is a good student and is particularly gifted in mathematics. He loves to solve mathematical problems that require him to think outside of the box. Therefore, his teacher presents him with the following riddle:
26 parameters (a to z) are given with the following values:
a = 1, b = 2, c = 3, d = 4, …, z = 26
Calculate the result of the following expressions:
(a – x) * (b – x) * (c – x) * (d – x) * … * (z – x) = ?
Help Marvin to solve this puzzler and find out how to get the answers in a particularly speedy way.
The solution of this calculation task becomes particularly clear when starting the multiplication backwards.
…. (w-x) * (x-x) * (y-x) * (z-x) = ?
As can be seen, the third to last expression is "(x-x)" which results in "0".
If one of the factors in the multiplication is "0", the result of the total multiplication is "0". Therefore, the solution of this task is "0", too.
If Martin recognizes this, he does not have to go through the complete calculation path to get to the solution.