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I will re-say the facts for you clearer: - Set of dominoes - No domino is the same - All possible tiles are chosen with the number of pips (dots) on either side being ranged 0-10 - How many dominoes per set? If you are still confused, what exactly are you confused on (would help make you less confused a lot)?
Grade 7/8 POTW: To do this POTW, I need to find the total number of possible tiles (if none repeat and all possible combinations were in this pack) in this 10 pack. For this, I can make a chart that shows all the possible tiles. (number on left side): (possible numbers for the right side) 0- 0,1,2,3,4,5,6,7,8,9,10 1- 1,2,3,4,5,6,7,8,9,10 2- 2,3,4,5,6,7,8,9,10 3- 3,4,5,6,7,8,9,10 4- 4,5,6,7,8,9,10 5- 5,6,7,8,9,10 6- 6,7,8,9,10 7- 7,8,9,10 8- 8,9,10 9- 9,10 10- 10 (notice how I didn't put both (0,1) and (1,0) because they are the same...) If I add up the total number of possible tiles, I get 66 :D
0: 0,1,2,3,4,5,6,7,8,9,10 1: 1,2,3,4,5,6,7,8,9,10 2: 2,3,4,5,6,7,8,9,10 3: 3,4,5,6,7,8,9,10 4: 4,5,6,7,8,9,10 5: 5,6,7,8,9,10 6: 6,7,8,9,10 7: 7,8,9,10 8: 8,9,10 9: 9,10 10: 10 There are 11 possibilities for 0, 10 for 1, 9 for 2, 8 for 3 and so on until 1 for 10. 11+10+9+8+7+6+5+4+3+2+1 = 66
So for this question, there are two parts. I first have to list all the possibilities for the number of pips on the dominoes, and from there I can figure out how many tiles are in the pack.
So instead of writing a huge list of numbers, I have come to the conclusion that for every number of domino (if that makes sense), the list of possibilities for pips can only start from that number, thus lessening the amount as number of dominos grows. For example, for the fifth pack, it must start at 5, and then go on until ten, it can't go back to 0.
So once I had all my possibilities out, I didn't realize that all I had to do was add up all the "packs" to get the number of tiles (I'm smart.....). This number was 66. Therefore there were 66 tiles or dominos in the ten pack!
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ReplyDelete?????????
DeleteHow?
Deletewait... I'm confused
DeleteI will re-say the facts for you clearer:
Delete- Set of dominoes
- No domino is the same
- All possible tiles are chosen with the number of pips (dots) on either side being ranged 0-10
- How many dominoes per set?
If you are still confused, what exactly are you confused on (would help make you less confused a lot)?
Grade 7/8 POTW
ReplyDeleteI forgot what this is called, but I just have to list all possibilities without repeating one which is the same thing as the 1 + 2 + 3 + 4 thing. 0-10 consists of 11 numbers. 1+2+3+4+5+6+7+8+9+10=66. A 10-set of dominoes consists of 66 dominoes. Here is a list of the possibilities:
1 0, 0
2 0, 1
3 0, 2
4 0, 3
5 0, 4
6 0, 5
7 0, 6
8 0, 7
9 0, 8
10 0, 9
11 0, 10
12 1, 1
13 1, 2
14 1, 3
15 1, 4
16 1, 5
17 1, 6
18 1, 7
19 1, 8
20 1, 9
21 1, 10
22 2, 2
23 2, 3
24 2, 4
25 2, 5
26 2, 6
27 2, 7
28 2, 8
29 2, 9
30 2, 10
31 3, 3
32 3, 4
33 3, 5
34 3, 6
35 3, 7
36 3, 8
37 3, 9
38 3, 10
39 4, 4
40 4, 5
41 4, 6
42 4, 7
43 4, 8
44 4, 9
45 4, 10
46 5, 5
47 5, 6
48 5, 7
49 5, 8
50 5, 9
51 5, 10
52 6, 6
53 6, 7
54 6, 8
55 6, 9
56 6, 10
57 7, 7
58 7, 8
59 7, 9
60 7, 10
61 8, 8
62 8, 9
63 8, 10
64 9, 9
65 9, 10
66 10, 10
Oi, yoi. Thats long..
DeleteNot really. I didn't indent like you so it isn't too long
DeleteGrade 7/8 POTW:
ReplyDeleteTo do this POTW, I need to find the total number of possible tiles (if none repeat and all possible combinations were in this pack) in this 10 pack.
For this, I can make a chart that shows all the possible tiles.
(number on left side): (possible numbers for the right side)
0- 0,1,2,3,4,5,6,7,8,9,10
1- 1,2,3,4,5,6,7,8,9,10
2- 2,3,4,5,6,7,8,9,10
3- 3,4,5,6,7,8,9,10
4- 4,5,6,7,8,9,10
5- 5,6,7,8,9,10
6- 6,7,8,9,10
7- 7,8,9,10
8- 8,9,10
9- 9,10
10- 10
(notice how I didn't put both (0,1) and (1,0) because they are the same...)
If I add up the total number of possible tiles, I get 66 :D
Grade 8 POTW:
ReplyDeleteHere are all the possibilities:
0: 0,1,2,3,4,5,6,7,8,9,10
1: 1,2,3,4,5,6,7,8,9,10
2: 2,3,4,5,6,7,8,9,10
3: 3,4,5,6,7,8,9,10
4: 4,5,6,7,8,9,10
5: 5,6,7,8,9,10
6: 6,7,8,9,10
7: 7,8,9,10
8: 8,9,10
9: 9,10
10: 10
There are 11 possibilities for 0, 10 for 1, 9 for 2, 8 for 3 and so on until 1 for 10.
11+10+9+8+7+6+5+4+3+2+1 = 66
There are 66 tiles in a set of dominoes.
POTW
ReplyDeleteSo for this question, there are two parts. I first have to list all the possibilities for the number of pips on the dominoes, and from there I can figure out how many tiles are in the pack.
So instead of writing a huge list of numbers, I have come to the conclusion that for every number of domino (if that makes sense), the list of possibilities for pips can only start from that number, thus lessening the amount as number of dominos grows. For example, for the fifth pack, it must start at 5, and then go on until ten, it can't go back to 0.
So once I had all my possibilities out, I didn't realize that all I had to do was add up all the "packs" to get the number of tiles (I'm smart.....). This number was 66. Therefore there were 66 tiles or dominos in the ten pack!
Grade 7/8 POTW
ReplyDeleteThere are 66 different tiles in the set of dominoes. I did my work on paper.
Grade 8 POTW
ReplyDeleteThere are 66 tiles in the 10 set of dominoes. I used factorials to figure this question out. My work is in my math notebook.
After simply calculating probabilities, I have determined that there would be 66 different tiles.
ReplyDeleteThere will be 66 tiles in the 10 set of dominoes by adding numbers 11 to 1 together to get 66
ReplyDelete66 tiles because you add all numbers from one to eleven.
ReplyDelete