Karl Guess
(Inspired by Carl Friedrich Gauss’s story)
One day a long time ago,
there was a 6th grader by the name of Karl Guess. Although he was a smart
student, his teacher disliked him because he misbehaved a lot. One day, because
he misbehaved during class, the teacher decided to outsmart Karl and ask him an
impossible question to work on to not disturb the class until it was over. The
teacher knew Karl was smart, so he decided to give a question that should take
hours to complete. He thought for a while before coming up with a question that
should take a long time to complete. He asked Karl to say the maximum amount of
5 digit numbers you can make without repeating any numbers. Satisfied with his
work, he resumed to teaching the class.
The teacher had a look
of shock on his face when he stood up and brought a piece of paper to his desk.
Written on it was the number 30,240. When the teacher asked what this was he
said it was the answer. Still shocked, the teacher asked how he got the answer,
and Karl started to explain: There are 5 digits. The first digit can hold one
of ten values: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The next digit can only hold
one of nine values because you can’t repeat the same number twice. Then the
next digit was one of eight and so on down to six. This is because there are
only 5 digits, and if the first digit can hold ten values, the next digit would
hold one less and so first it would be one of 10, then 9, then 8, then 7, then
finally one of 6 values. Then all that was left to do was multiply these
numbers resulting in 30,240. Then he showed how he solved it on a piece of
paper:
(10*9*8*7*6*5*4*3*2*1)
/ (5*4*3*2*1) = 30,240
That day, Karl shocked the whole class by solving a
question not even the teacher couldn’t solve before Karl explained it to him.
From that day on, the teacher saw Karl in a new light.
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