9
$\begingroup$

Using the digits from $1$ to $9$,

  • Form four numbers, such as ($X$,$Y$,$Z$,$T$)
  • Then take $X\div Y$ and $Z\div T$ where both values should be different than each other.
  • You need to use all digits from $1$ to $9$ but once, such as ($923\div 85$,$67\div 41$)

What is the smallest difference between these two values?

$\endgroup$
  • $\begingroup$ how many digits for each number, any restrictions? $\endgroup$ – Shahriar Mahmud Sajid Sep 17 '18 at 11:24
  • $\begingroup$ Strange you accepted the answer that provided solution later. $\endgroup$ – rus9384 Sep 17 '18 at 19:05
  • $\begingroup$ @rus9384 what do you mean by solution later? $\endgroup$ – Oray Sep 17 '18 at 19:05
  • $\begingroup$ See when the edits were commited. Just hover your mouse over "edited x hours ago" link. $\endgroup$ – rus9384 Sep 17 '18 at 19:06
  • $\begingroup$ @rus9384 seems you are right, I missed the other one who provided the right answer before anyone else :) thanks $\endgroup$ – Oray Sep 17 '18 at 19:08
12
$\begingroup$

My first attempt

Staying close to the original order of numbers
45/69 - 78/123
0.01802757

No major breakthrough, just another attempt

Keeping the top low and using ad odd number of total top digits
12/987 - 5/436
0.000690164803

Third

2/835 - 4/1679
0.00001283912223

This one is pretty small

Again keeping the top tiny and trying to keep the bottom factor as close to the factor on top
1 / 826 - 9 / 7435
0.000000162831708
(7435 / 826 = 9.00121)

$\endgroup$
  • 2
    $\begingroup$ I wrote a computer program, and your last solution seems to be the best possible. $\endgroup$ – Jaap Scherphuis Sep 17 '18 at 13:02
  • $\begingroup$ @JaapScherphuis yes, I did the same and it doesn't get lower than that $\endgroup$ – NoOorZ24 Sep 17 '18 at 13:13
  • 1
    $\begingroup$ As this one got smallest possible answer 1st I think this should be accepted $\endgroup$ – NoOorZ24 Sep 17 '18 at 13:14
  • 1
    $\begingroup$ I feel I got a bit lucky here, as @Bass inspired my approach and the factor chosen was a bit arbitrary. Anyway, fun puzzle. It made quite a few people push for perfection, and the improvement of answers from different people was fun to see! $\endgroup$ – MKBakker Sep 17 '18 at 13:19
  • $\begingroup$ By the way, I took a look at all the non-answers where the difference is zero. These range from $1/8 - 954/7632=0$ where there is a factor of $954$ between their denominators or numerators, to $32/96 - 58/174=0$ where the factor is just below $2$. $\endgroup$ – Jaap Scherphuis Sep 17 '18 at 14:57
10
$\begingroup$

First attempt:

Make two rational numbers, with one's numbers twice that of the others, small numbers on top, large numbers on the bottom: $\frac{4}{763} - \frac{8}{1529} \approx .000010 $ (four zeroes after the decimal point)

Second attempt:

Factor of three: $\frac{1}{954} - \frac{3}{2867} \approx .0000018 $ (five zeroes)

Third:

$\frac{4}{3567} - \frac{1}{892} \approx .000000314 $ (six zeroes)

Fourth:

$\frac{1}{826} - \frac{9}{7435} \approx .00000016 $ (still six zeroes)

$\endgroup$
5
$\begingroup$

I think it might be

0.

This is because

$\frac{1358}{4} - \frac{679}{2} = 0$.

$\endgroup$
  • 1
    $\begingroup$ "both values should be different than each other." $\endgroup$ – Oray Sep 17 '18 at 12:38
  • $\begingroup$ given that the values must be different, 0 seems unlikely. $\endgroup$ – Bass Sep 17 '18 at 12:38
  • 1
    $\begingroup$ Sorry gentlemen, I just can’t read! $\endgroup$ – El-Guest Sep 17 '18 at 12:38
  • $\begingroup$ though still thumps up, good one :) $\endgroup$ – Oray Sep 17 '18 at 12:46
5
$\begingroup$

Joke answer.

You guys are going about this all wrong. Clearly the answer is:
$$\frac{2}{3}-\frac{987654}{1} = -987653.333\ldots$$ This is much smaller than your near zero answers.

$\endgroup$
  • $\begingroup$ Hahahahahahaha. Hilarious! Good one! Although technically a whole number is a fraction, and he didn't say we can't do exponents, so, 1 - (9^8^7^6^5^4^3^2) is way better. $\endgroup$ – Alto Sep 17 '18 at 17:18
4
$\begingroup$

Just by randomly mixing up different digits I came up with this

$\dfrac{64}{8} - \dfrac{975}{123} = 0.0731707\dots$

Second try

$\dfrac{124}{975} - \dfrac{8}{63} = 0.000195\dots$

$\endgroup$
  • $\begingroup$ You can do much better by using the reciprocal values. $\endgroup$ – M Oehm Sep 17 '18 at 11:56
  • $\begingroup$ @MOehm oh god, thats true, feel stupid now $\endgroup$ – Ian Fako Sep 17 '18 at 11:58
2
$\begingroup$

Here's My attempt-

$\dfrac{975}{483} - \dfrac{12}{6} = 0.01863354\dots$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.