Expert: Lynn Houston - 12/14/2008

Question
I have a number puzzle for my little brother's math homework (sad story, I'm 25, he's 10!). I have a triangle with a '?' at each point. The number I have to reach is 600. There has to be a difference between each number, the differences are:

    10 \
     |  \
     |   20
     |  /
    30 /

For example, I can use 200, 190, 220 = 610, or 190, 180, 210 = 580. I've been told he can't use decimals so whole numbers only, but I really can't think of way to lose that 10, or gain 20 to make 600.

Please help!

Thanks :)


Answer
There's no way to do it without decimals.

Algebraically, the eq is
a+b+c = 600
b-a = 10 or b=10+a
c-b = 20 or c=20+b
c-a = 30 or c=30+a

insert 2nd and 4th into first eq.

a+10+a+30+a = 600
3a + 40 = 600
3a = 560
a = 186.66667
b = 196.66667
c = 216.66667