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The sponsor of a basketball team has offered 209 branded t-shirts to the regional high school players. Each of the t-shirts had a unique number from 2 to 210 printed on its back.
In order to randomly assign the t-shirts to the students, the kids were all given a unique number from 1 to 209 and the shirts would be randomly assigned by carrying out some kind of draw. The maths teacher, however, decided to make it a bit more tricky, so he asked the students to find a way to assign the shirts in such a way, that each student's number is a factor of the t-shirt's number. He then asked them to find how many such ways there are and also to give an example of such an arrangement (we remind that each number has at least two factors, 1 and the number itself).
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Last edited by thickhead (2016-10-03 19:43:11)
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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Most of the players have to be given T shirt with the same number as the student number.Minimum of one student and at the most 4 will be given shirts of different number. There are 75 ways and are given below.
NO. Student No T shirt No.
1 105 210
1 105
2 105 210
35 105
1 35
3 105 210
35 105
7 35
1 7
4 105 210
35 105
5 35
1 5
5 105 210
21 105
1 21
6 105 210
21 105
7 21
1 7
7 105 210
21 105
3 21
1 3
8 105 210
15 105
1 15
9 105 210
15 105
5 15
1 5
10 105 210
15 105
3 15
1 3
11 105 210
7 105
1 7
12 105 210
5 105
1 5
13 105 210
3 105
1 3
14 70 210
1 70
15 70 210
35 70
1 35
16 70 210
35 70
7 35
1 7
17 70 210
35 70
5 35
1 5
18 70 210
14 70
1 14
19 70 210
14 70
7 14
1 7
20 70 210
14 70
2 14
1 2
21 70 210
10 70
1 10
22 70 210
10 70
5 10
1 5
23 70 210
10 70
2 10
1 2
24 70 210
7 70
1 7
25 70 210
5 70
1 5
26 70 210
2 70
1 2
27 42 210
1 42
28 42 210
21 42
1 21
29 42 210
21 42
7 21
1 7
30 42 210
21 42
3 21
1 3
31 42 210
14 42
1 14
32 42 210
14 42
7 14
1 7
33 42 210
14 42
2 14
1 2
34 42 210
7 42
1 7
35 42 210
6 42
1 6
36 42 210
6 42
3 6
1 3
37 42 210
6 42
2 6
1 2
38 42 210
3 42
1 3
39 42 210
2 42
1 2
40 35 210
1 35
41 35 210
7 35
1 7
42 35 210
5 35
1 5
43 30 210
1 30
44 30 210
15 30
1 15
45 30 210
15 30
5 15
1 5
46 30 210
15 30
3 15
1 3
47 30 210
10 30
1 10
48 30 210
10 30
5 10
1 5
49 30 210
10 30
2 10
1 2
50 30 210
6 30
1 6
51 30 210
6 30
3 6
1 3
52 30 210
6 30
2 6
1 2
53 30 210
5 30
1 5
54 30 210
3 30
1 3
55 30 210
2 30
1 2
56 21 210
1 21
57 21 210
7 21
1 7
58 21 210
3 21
1 3
59 15 210
1 15
60 15 210
5 15
1 5
61 15 210
3 15
1 3
62 14 210
1 14
63 14 210
7 14
1 7
64 14 210
2 14
1 2
65 10 210
1 10
66 10 210
5 10
1 5
67 10 210
2 10
1 2
68 7 210
1 7
69 6 210
1 6
70 6 210
3 6
1 3
71 6 210
2 6
1 2
72 5 210
1 5
73 3 210
1 3
74 2 210
1 2
75 1 210{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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@thickhead: You are a genius!!
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