rmo hahahahaha
5 posters
Science for Fun :: Level 1 , 2 and 3 :: Olympiad :: Maths
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rmo hahahahaha
rmo1993
find
1. Positive integers are written on all the faces of a cube, one on each. At each corner (vertex)
of the cube, the product of the numbers on the faces that meet at the corner is written. The
sum of the numbers written at all the corners is 2004. If T denotes the sum of the numbers
on all the faces, find all the possible values of T.
find
1. Positive integers are written on all the faces of a cube, one on each. At each corner (vertex)
of the cube, the product of the numbers on the faces that meet at the corner is written. The
sum of the numbers written at all the corners is 2004. If T denotes the sum of the numbers
on all the faces, find all the possible values of T.
Re: rmo hahahahaha
Is it level 0???????
i'll try(though i am sure I can't solve)
(just checking the smileys)
i'll try(though i am sure I can't solve)
(just checking the smileys)
Re: rmo hahahahaha
Place the cube on the ground. Call the faces perpendicular to the ground a,b,d,e with b parallel to e and a parallel to d, the face on the ground c and the one on the top f.
We have
abc+bcd+bfd+fed+fab+aec+efd+cde=2004
(c+f)(a+d)(b+e)=2004
Now 2004=2.2.3.167
So
2004=2.2.501 This gives a+b+c+d+e+f=505
2004=3.2.334 This gives a+b+c+d+e+f=339
2004=2.6.167 This gives a+b+c+d+e+f=175
2004=3.4.167 This gives a+b+c+d+e+f=174
We have
abc+bcd+bfd+fed+fab+aec+efd+cde=2004
(c+f)(a+d)(b+e)=2004
Now 2004=2.2.3.167
So
2004=2.2.501 This gives a+b+c+d+e+f=505
2004=3.2.334 This gives a+b+c+d+e+f=339
2004=2.6.167 This gives a+b+c+d+e+f=175
2004=3.4.167 This gives a+b+c+d+e+f=174
paranormal- Number of posts : 7
points :
Registration date : 2008-10-21
Re: rmo hahahahaha
tell neone brougth u here or u came to know by yourself(searching on d web)...........well still welcome to sff..........
Re: rmo hahahahaha
How did you know, you cunning ass? <-----Do you know my password? or did you hack my account somehow??
paranormal- Number of posts : 7
points :
Registration date : 2008-10-21
Science for Fun :: Level 1 , 2 and 3 :: Olympiad :: Maths
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