Math Problem!

Alright, here is a math problem. In order to get full credit, you should be able to justify your answer.
Find the largest integer D such that

1/A + 1/B + 1/C + 1/D = 1

Where 0<A<B<C<D

Quote: cardshark

Alright, here is a math problem. In order to get full credit, you should be able to justify your answer.
Find the largest integer D such that

1/A + 1/B + 1/C + 1/D = 1

Where 0<A<B<C<D

(BCD + ACD + ABD + ABC) / ABCD

Give us a hard one!

EDIT: Oops, I thought you meant an equivalent fraction to 1/A + 1/B + 1/C + 1/D, sorry! Got ahead of myself!

Quote: cardshark

Alright, here is a math problem. In order to get full credit, you should be able to justify your answer.

My answer is 42, and I am able to justify it :)

Quote: weaselman

My answer is 42, and I am able to justify it :)

Yes, the answer is 42. Care to share your explanation as to why there is no larger D?

We are looking for such A, B and C that 1/A+1/B+1/C is the largest possible value less than 1.

If I knew the smallest C such that 1/a + 1/b + 1/c = 1, then d would be 1/c-1/(c+1).
If I knew the smallest b such that 1/a + 1/b = 1, then 1/c I am looking for would be 1/b-1/(b+1).
If I knew the smallest a such that 1/a=1, then 1/b I need would be 1-1/(a+1).

I do know the a - it's 1. Thus, b = 2, c = 6, d=42.

(note the actual values for A, B and C are 1 higher than a,b,c above (2,3,7) because the partial sums need to be less then than 1, not equal)

Quote: weaselman

We are looking for such A, B and C that 1/A+1/B+1/C is the largest possible value less than 1.

If I knew the smallest C such that 1/a + 1/b + 1/c = 1, then d would be 1/c-1/(c+1).
If I knew the smallest b such that 1/a + 1/b = 1, then 1/c I am looking for would be 1/b-1/(b+1).
If I knew the smallest a such that 1/a=1, then 1/b I need would be 1-1/(a+1).

I do know the a - it's 1. Thus, b = 2, c = 6, d=42.

(note the actual values for A, B and C are 1 higher than a,b,c above (2,3,7) because the partial sums need to be less then than 1, not equal)

Well done!