How do you use all 10 digits to form a fraction equivalent to one half?

Answer 1

Questions like this are so interesting and fun! There are probably good, logical, intelligent approaches to use, but I resorted to checking all the possible numerators with a computer. The numerators which (together with their corresponding denominators) used all ten digits were output. And here are the solutions. There are 48!! 13485 / 26970 = 0.5

13548 / 27096 = 0.5

13845 / 27690 = 0.5

14538 / 29076 = 0.5

14685 / 29370 = 0.5

14835 / 29670 = 0.5

14853 / 29706 = 0.5

14865 / 29730 = 0.5

15486 / 30972 = 0.5

16485 / 32970 = 0.5

18546 / 37092 = 0.5

18645 / 37290 = 0.5

20679 / 41358 = 0.5

20769 / 41538 = 0.5

20793 / 41586 = 0.5

23079 / 46158 = 0.5

26709 / 53418 = 0.5

26907 / 53814 = 0.5

27069 / 54138 = 0.5

27093 / 54186 = 0.5

27309 / 54618 = 0.5

29067 / 58134 = 0.5

29073 / 58146 = 0.5

29307 / 58614 = 0.5

30729 / 61458 = 0.5

30792 / 61584 = 0.5

30927 / 61854 = 0.5

31485 / 62970 = 0.5

32079 / 64158 = 0.5

32709 / 65418 = 0.5

32907 / 65814 = 0.5

34851 / 69702 = 0.5

35148 / 70296 = 0.5

35481 / 70962 = 0.5

38145 / 76290 = 0.5

38451 / 76902 = 0.5

45138 / 90276 = 0.5

45186 / 90372 = 0.5

45381 / 90762 = 0.5

46185 / 92370 = 0.5

46851 / 93702 = 0.5

48135 / 96270 = 0.5

48351 / 96702 = 0.5

48513 / 97026 = 0.5

48516 / 97032 = 0.5

48531 / 97062 = 0.5

48615 / 97230 = 0.5

48651 / 97302 = 0.5 (A mistake with the code first time around led to several wasted hours trying to find a concise proof that the problem was impossible - which it clearly isn't!)