Est. 1998 — 27 years of woodworking knowledge
Friday puzzle on Saturday
A little late, but each letter below represents a different digit, 1-9. Find them.
A/BC + D/EF + G/HI = 1
There are six solutions, but they are just permutations of the addends, so to make it unique, add the condition that A <D < G.
PS: BC represents a two digit number, such as 24, not a product such as 2*4.
Starting point?
I figured that since they are fractions, and if the denominators get too big, it would be hard to get to a sum of one, a potential starting point would be the largest fraction that I could make, which would be 9/12. This then requires two other fractions using the numbers left that add to 1/4.
And a good starting point it is
A bit farther
The other two denominators have to be multiples of each other with a common denominator that is a multiple of 4. (adds to 1/4) You have to be able to get a common denominator that enables you to add them to 1.
Half right
But I don't wee your reasoning for the GCD of the denominators being a multiple of four. 1/6 + 1/12 = 1/4, but GCD of 6 and 12 is not a multiple of 4.
Re: Half right
12 has a 4 in it, so any common denominator for 12 would also have to contain a 4. ;-)
how about this?
9/12 +7/68 + 5/34 =1
Semantics?
Been 45 years since I learned these terms, so I may well have it messed up!
I thought GCD of 12 and 6 was the largest number that divided into both, i.e. 6.
The LCM (least common multiple) would be 12.
But, semantics aside, you got the answer. Nice job!
Yes!
Nice job.
I'll give you a pass on the order of the terms.
Re: Semantics?
I was thinking of lowest common denominator, not divisor. I think that was the difference.
OOPS
I posted it without looking at the question again. I was thinking A > B >: C ;-)
And you were right
What the heck, it feels good to shake the rust off of this stuff even if it involves making a mistake that my 6th-grade niece or nephew would probably call me on!
Re: And you were right
That is one of the things that I enjoy about the trivia and the puzzles. It makes me think and review stuff I either did learn, or was supposed to have learned in school.