Open Middle®
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.
21/35 = 60% like that?
The marking is clearly to the right of 50 %, leaving us with
09 = 75 % of 12
13 = 65 % of 20
17 = 85 % of 20
18 = 75 % of 24
17 = 68 % of 25
19 = 76 % of 25
21 = 60 % of 35
38 = 95 % of 40
27 = 60 % of 45
36 = 80 % of 45
36 = 75 % of 48
31 = 62 % of 50
32 = 64 % of 50
34 = 68 % of 50
36 = 72 % of 50
38 = 76 % of 50
39 = 78 % of 50
41 = 82 % of 50
43 = 86 % of 50
46 = 92 % of 50
48 = 96 % of 50
63 = 84 % of 75
76 = 95 % of 80
63 = 75 % of 84
76 = 80 % of 95
I counted the whole line segment to be 645 pixels long and the segment between 0 % and _ _ % to be 410 pixels long, so the line segment is split into two parts, with the length of the left one being 410/645 % of the whole segment, which is about 64 %. The solution that fits the image best is therefore 32 = 64 % of 50
09 is 12% and 36 is 48% both of 75
are two solutions that use all the digits 0-9 once only together on a single number line