Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create an accurate number line. How many solutions can you find?

### Hint

Encourage students to try different approaches to find multiple answers.

Fill in the percent and the part and calculate whole values.

Fill in percent and whole value and calculate the part.

### Answer

Number of Unique Solutions: 64

1: 13/20 = 65%

2: 13/26 = 50%

3: 13/50 = 26%

4: 13/65 = 20%

5: 14/28 = 50%

6: 14/50 = 28%

7: 16/32 = 50%

8: 16/50 = 32%

9: 17/20 = 85%

10: 17/25 = 68%

11: 17/34 = 50%

12: 17/50 = 34%

13: 17/68 = 25%

14: 17/85 = 20%

15: 18/24 = 75%

16: 18/36 = 50%

17: 18/50 = 36%

18: 18/75 = 24%

19: 19/25 = 76%

20: 19/38 = 50%

21: 19/50 = 38%

22: 19/76 = 25%

23: 21/35 = 60%

24: 21/60 = 35%

25: 23/46 = 50%

26: 23/50 = 46%

27: 27/45 = 60%

28: 27/60 = 45%

29: 31/50 = 62%

30: 31/62 = 50%

31: 32/50 = 64%

32: 32/64 = 50%

33: 34/50 = 68%

34: 34/68 = 50%

35: 36/45 = 80%

36: 36/48 = 75%

37: 36/50 = 72%

38: 36/72 = 50%

39: 36/75 = 48%

40: 36/80 = 45%

41: 38/40 = 95%

42: 38/50 = 76%

43: 38/76 = 50%

44: 38/95 = 40%

45: 39/50 = 78%

46: 39/78 = 50%

47: 4/16 = 25%

48: 4/25 = 16%

49: 41/50 = 82%

50: 41/82 = 50%

51: 43/50 = 86%

52: 43/86 = 50%

53: 46/50 = 92%

54: 46/92 = 50%

55: 48/50 = 96%

56: 48/96 = 50%

57: 63/75 = 84%

58: 63/84 = 75%

59: 76/80 = 95%

60: 76/95 = 80%

61: 9/12 = 75%

62: 9/25 = 36%

63: 9/36 = 25%

64: 9/75 = 12%

Source: Adrianne Burns

60%, 21, 35

58%

9/75=12%

9/75= 12%

I still don´t really understand this after the video I watched but I´m gonna say that the two boxes together are 90% and 90??

9/75=12%

9/12 75%

13/20 = 65%

Divide sets of two digit numbers where the smaller is more than half the larger and all four digits are different.

(ie 24/35, 25/34, 15/23, 16/24) and check if the percentage has unique digits from the 4 already used.

24/35 = 69% YES, 25/34 = 74% NO, 15/23 = 65% NO, 16/24 = 67% NO

25/39 = 64% YES

Not sure of a faster way to find all solutions other than writing a program to brute force it.