BdMO National 2013: Primary 3

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BdMO
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BdMO National 2013: Primary 3

Unread post by BdMO » Fri Jan 10, 2014 1:13 am

A cube-shaped room has six walls (floor, roof and east, west, north, south walls). A grasshopper is sitting at the south-west corner of the floor. The grasshopper needs to go to the north-east corner of the roof by jumping upward, northward or eastward and in each jump it goes one-third of the room's length. If the grasshopper gets $5$ points for each upward jump, $3$ points for each eastward jump and $1$ point for each northward jump, then what is the difference of the maximum and the minimum number of points it can have when it reaches its destination?

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samiul_samin
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Re: BdMO National 2013: Primary 3

Unread post by samiul_samin » Fri Feb 16, 2018 8:51 am

Hint
It should jump at least 9 times.
Answer
0

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samiul_samin
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Re: BdMO National 2013: Primary 3

Unread post by samiul_samin » Fri Feb 16, 2018 8:55 am

Solution
In any way it jumps,it should jump thrice in all three directions and will get the same point every time.
So, highest point=lowest point
The answer is $\fbox 0$

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