Saturday, July 4, 2015

Fourth of July Puzzle

Out of Many, One

In the Constitution that was adopted in Philadelphia in 1787, there appear the following fractions:
3/5, 1/3, 2/3, 2/3, 2/3, 2/3, 2/3, 3/4.
For example, the fraction 3/5 appears infamously in Article I, Section 2, while the fraction  3/4 appears in Article V.

Challenge: Form 1 out of these fractions by using the operations of addition, subtraction, multiplication, and/or division.

In other words, create an expression, the value of which is 1, using all of the above fractions together with any or all of the symbols \(+\), \(-\), \(\times\), \(\div\), and parentheses.

3 comments:

jeff said...

(2/3 ÷ 3/5) + (2/3 ÷ 3/4) - (2/3 ÷ 1/3) + (2/3 ÷ 2/3) = 1

Thanks to some Excel gruntwork, i noticed that the first 2 parentheticals result in
10/9 + 8/9 = 2

I'd never have seen that without calculating every combination of +, -, ×, and ÷. Pretty coolio.

JasonZimba said...

Nice solution - and better than my own, because I believe I used 8 binary operations whereas you only used 7. (I also used parentheses in an essential way, whereas your parentheses are just for clarity.)

JasonZimba said...

Actually I used 7 binary operation symbols too - but the point about the parentheses still stands.