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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Comments
a circle is also a line and depending on the circumference of the circle the grasshopper could have landed on the starting point a number of times during the exercise
Hey, you've had some good teasers. But sorry to say - this is not one of them.
I've got to agree with tpg76 - I would be more specific, but everytime I do, I get whacked with more bad karma Send this one to the recycler
I sat down to do all the math, and finally decided the answer had something to do with the grasshopper's length. For me, your solution left me feeling let down - it wasn't as clever as what one might expect from a riddle of this kind, although I'd be hard-pressed to explain why on-the-spot.
this was dink of ambiguous
hop usually means in a forward or backward direction
hop usually means in a forward or backward direction
not only is a circle a line, but it didn't say the grasshopper stayed on the line and didn't turn between hops.
Bad,because you said "and so on"
Please feel free to make the corrections you desire.
I thought it was pretty good.I guess I'm not really picky
I dislike most questions in the Trick category. Either they are blindingly obvious or completely opaque. Here, you lulled us into complacency with the "and so on", then wrote the 9th hop differently. Everyone who didn't notice you wrote the 9th hop differently (including me ) was successfully tricked.
Fooled once again!
Wow! Good one! I suck at trick teasers, though...
i didn't get it...
wow. i did NOT like that one. what did the answer have to do with being even? i thought he supposedly landed on the starting point? either way, it was kind of =P
makes absolutely no sense at all...
Too lazy to mathematize. I'm linguistically minded as I have stated previously in other teasers somewhere. Oh well, sure it must have been fun.
If the grasshopper was on a hoop, that was somehow suspended in the air, and the hoop had a circumference of 45cm, then the grasshopper would land back where he started. I could then understand the answer. I don't understand your answer?
lol ya i was thinkin he was jumping in a circle..
I'm sorry to say this isn't one of my favorites, but I have to admit it was interesting.
He jumped forward 18 cm, then he jumped backward 18cm, and then he jumped staight up in the air. He landed on his starting point.
Sep 22, 2008
yes i am correct ^^ it jumped on its same place
It could also do this:
forward 1
forward 2
backward 3
forward 4
forward 5
backward 9
It never said it went 6, 7, or 8 hops forward/backward!
forward 1
forward 2
backward 3
forward 4
forward 5
backward 9
It never said it went 6, 7, or 8 hops forward/backward!
This teaser gave me a nosebleed!
Good Teaser! Don't imply that all his jumps have to be exclusively forward or backward on that number of jumps. He can mix it up...like say on his 6th jump he can go 3 forward and 3 backward. Therefore, as long as the grand total number of jumps is an even number he can end up at the starting point (1+2+3+4+5+6+7+8=36 EVEN) and if you pay attention, the TRICK was the 9th jump when he never actually said anything about it having to be forward or backward. Again, Good Teaser! People are just mad at themselves for being tricked.
Wow I just spent all that time defending it and now I see the problem with it. On the 6th jump (as in my last example) it wasn't (6) 1 centimeter jumps but (1) 6 centimeter jump. Therefore I really don't see HOW he ended up at the starting point. And the answer doesn't explain it at all.
i did the same thing as puppylover.
When I first read the answer, i thought it wasn't very clever. But the more i think about it, it is a pretty good teaser!
I thought it hopped 9 cm twice (ninth and last).
belongs in the other category
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