Brain Teasers
The Grasshopper
A grasshopper is standing on a thin line, and it hops.
The first time it hops 1 centimeter either forward or backward, the second time it hops 2 centimeters either forward or backward, the third time it hops 3 centimeters either forward or backward, and so on. The ninth and last time it hops 9 centimeters, and it ends up landing on its starting point.
How can this be possible?
The first time it hops 1 centimeter either forward or backward, the second time it hops 2 centimeters either forward or backward, the third time it hops 3 centimeters either forward or backward, and so on. The ninth and last time it hops 9 centimeters, and it ends up landing on its starting point.
How can this be possible?
Hint
If you think normally, 1+2+3+...+9=45 is odd, and the total distance it hopped forward can't equal the total distance it hopped backward.However, look at its category.
Answer
I didn't say it hopped either forward or backward the last time. In fact, in the last time, it hopped upward into the air.Therefore, the distance it hopped forward or backward is 45-9=36 centimeters, which is even.
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