Solve this impossible mensa problem for 10 points?

Question

Using numbers from 1 to 9, express 1/2. You can't repeat any of the numbers and must use ALL of them (1,2,3,4,5,6,7,8,9). It also must be a whole number.

Example 1: 23/46 = 1/2. In this case I used 2,3,4 and 6 to express 1/2. So write the answer as a fraction but follow the above rules.

Example 2: No adding, you must do it list the fraction like this:
1467/59823 < I used all the numbers as you can see. This fraction expresses .024, but you must express 1/2. Basically, in the fraction ALL of the numbers must be present.

Show how you figured this out if possible (I already know the answer btw). You can guess&check if you want, but there are millions of guesses you will have to go through.

Answer 1

There are several solutions:
6729/13458
6792/13584
6927/13854
7269/14538
7293/14586
7329/14658
7692/15384
7923/15846
7932/15864
9267/18534
9273/18546
9327/18654

Answer 2

Well, I solved it. There are twelve solutions:

6729 / 13458 = 1/2
6792 / 13584 = 1/2
6927 / 13854 = 1/2
7269 / 14538 = 1/2
7293 / 14586 = 1/2
7329 / 14658 = 1/2
7692 / 15384 = 1/2
7923 / 15846 = 1/2
7932 / 15864 = 1/2
9267 / 18534 = 1/2
9273 / 18546 = 1/2
9327 / 18654 = 1/2

I solved this using a computer program which iterated i from 6000 to 9999. It found 2*i, then counted the number of copies of each digit 1 through 9 found in both i and 2*i. When it finds a value of i such that i and 2*i contain exactly one each of each digit between them, it prints out i and 2*i.

That was a fun problem. Got any more?

Answer 3

I got 7932/15864 by reducing.

easily the 1 goes first digest denominator. This puts the 5 in a certain position, it has to go in the denomiator or we would get a 0 or 1 in the denominator. Also 5 can't go as last digit denomiator. The lower numbered evens are easy to play with so then I considered where to put 5, 7, 8, 9. Since the first digets wont relay on the last two if they are small enough, this left me with just figuring out where to put 5, ,7,8,9. since 8 is even I put it as the third in denomiator and that puts 9 second numerator. Then well there is nothing left to guess.

Answer 4

the component of the outdoor is going to be some subject squared (with the aid of way of actuality it particularly is a sq. outdoor quite than using Width * length we are waiting to certainly use length * length and make it much less complicated) a=L^2 the component of the sidewalk is although the dimensions is, circumstances width (2) b=2y the are equivalent 2y=L^2 we additionally comprehend the the dimensions of the sidewalk is 4 circumstances the dimensions of the outdoor with the aid of way of actuality it is going around it on 4 aspects 2(4L)=L^2 yay in person-friendly words one variable 8L=L^2 tempting to divide of L on the two aspects yet that often motives matters quite basically pass each little subject to a minimum of one area 0=L^2-8L or extra advantageous in many circumstances used... L^2-8L=0 finished the sq. L^2-8L+(4^2)=(4^2) (L-4)^2=sixteen sq. root the two aspects L-4=4 L=8 it particularly is what we'd are starting to be if we divided off the L before yet now and decrease back that motives matters and we finally finally end up with an unsolvable difficulty ok so the sq. outdoor is 8 meters long, (and hence 8 meters extensive) so 8*8=sixty 4 sixty 4 sq. meters assuming i did not make an arithmetic mistake

Answer 5

9327 / 18654

9 = ½ ( 18 )

3 = ½ ( 6 )

27 = ½ ( 54 )