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#1 2016-10-02 04:58:09

salem_ohio
Member
Registered: 2016-03-11
Posts: 37

Basketball t-shirts

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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#2 2016-10-02 18:18:46

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Basketball t-shirts

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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#3 2016-10-03 21:12:44

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Basketball t-shirts

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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#4 2016-10-12 00:03:14

salem_ohio
Member
Registered: 2016-03-11
Posts: 37

Re: Basketball t-shirts

@thickhead: You are a genius!!

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