Enjoy the PA day today folks! (Oct. 20th).
P.S. To be honest I (Mr. Milette) was not a fan of the question for this week for Gr. 9/10 (which I usually post as the "Grade 8 POTW" and it involved two fairly large images to be posted. Thus, there is one question this week. Both Grades please answer the following:
POTW #7 Grade 7/8 Question:
POTW #6 Solution:
The Beaver Rangers will be BR and the Fox Raiders will be FX.
ReplyDelete6 points were scored in total, and the numbers do not have to be even.
Point number scored (Way #1):
BR: 1, 2, 4, 5,
FR: 3, 6,
#2:
BR: 1, 3, 5,
FR: 2, 4, 6,
#3
BR:1, 3, 4,
FR: 2, 5, 6,
#4
BR: 1, 3, 6,
FR: 2, 4, 5
Those were all the choices I could think of, but I know that I could switch the points scored. That means that there would be 4 options. I also found another way to solve this question.
_ _ _ _ _ _
For the first goal, 2 teams could’ve gotten them, Same with the second. But on the third one, since no one scored three points in a row, only one team could’ve scored it. Then I just repeated the pattern for the rest of the spaces.
2 x 2 x 1 x 2 x 2 x 1 = 8
POTW
ReplyDeleteFirst, I’ll list the facts.
- BR vs FX
- 6 goals total
- No team scored 3 in a row
- All possible scores
- All possible ways BR wins
I will now list the possibilities. BR=1 FX=2
The right side shows who wins.
1, 1, 2, 1, 1, 2 BR
1, 1, 2, 1, 2, 1 BR
1, 1, 2, 1, 2, 2 Tie
1, 1, 2, 2, 1, 1 BR
1, 1, 2, 2, 1, 2 Tie
1, 2, 1, 1, 2, 1 BR
1, 2, 1, 1, 2, 2 Tie
1, 2, 1, 2, 1, 1 BR
1, 2, 1, 2, 1, 2 Tie
1, 2, 1, 2, 2, 1 Tie
1, 2, 2, 1, 1, 2 Tie
1, 2, 2, 1, 2, 1 Tie
1, 2, 2, 1, 2, 2 FX
2, 1, 2, 1, 1, 2 Tie
2, 1, 2, 1, 2, 1 Tie
2, 1, 2, 1, 2, 2 FX
2, 1, 2, 2, 1, 1 Tie
2, 1, 2, 2, 1, 2 FX
2, 1, 1, 2, 1, 2 Tie
2, 1, 1, 2, 2, 1 Tie
2, 1, 1, 2, 1, 1 BR
2, 2, 1, 1, 2, 1 Tie
2, 2, 1, 1, 2, 2 FX
2, 2, 1, 2, 1, 1 Tie
2, 2, 1, 2, 1, 2 FX
2, 2, 1, 2, 2, 1 FX
There are 26 possibilities.
If it is completely random and all the possibilities have an equal chance, then BR wins 6/26 times or 6 times.
1, 1, 2, 1, 1, 2
1, 1, 2, 1, 2, 1
1, 1, 2, 2, 1, 1
1, 2, 1, 1, 2, 1
1, 2, 1, 2, 1, 1
2, 1, 1, 2, 1, 1
I'm pretty sure this is right. I did it one by one though and I did NOT use a formula, even to check. However, I did re-check multiple times and added more possibilities each time. If I realize I had missed some, I'd correct it (unless the answer has been published and we're on the next POTW).
Mr Milette. If we were to create a POTW question, would it have to relate to the unit or can we just make any question?
DeleteAny question!
DeleteBeaver Rangers = 1
ReplyDeleteFox Raiders = 2
6 goals scored
Beaver Rangers won the game
No team scored 3 goals in a row
I wrote all the possibilities down in my math notebook.
There are 26 possible outcomes and out of them, the Beaver Rangers can win in 6 of them.
Bhavee's POTW #7
ReplyDeleteThere are 26 possibilities and I have 6 possible outcome of the Beaver Rangers winning (in my notebook)
Beaver Rangers: 1, Fox Raiders: 2
ReplyDeletenow I will list all possible option for goals scored in the game while both teams not having 3 goals in a row.
wins:
1, 1, 2, 1, 1, 2
1, 1, 2, 1, 2, 1
1, 1, 2, 2, 1, 1
1, 2, 1, 1, 2, 1
1, 2, 1, 2, 1, 1
2, 1, 1, 2, 1, 1
ties:
2, 2, 1, 2, 1, 1
2, 2, 1, 1, 2, 1
2, 1, 1, 2, 1, 2
2, 1, 1, 2, 2, 1
2, 1, 2, 2, 1, 1
2, 1, 2, 1, 2, 1
2, 1, 2, 1, 1, 2
1, 2, 2, 1, 2, 1
1, 2, 1, 2, 1, 2
1, 2, 1, 2, 2, 1
1, 2, 1, 1, 2, 2
1, 1, 2, 2, 1, 2
1, 1, 2, 1, 2, 2
loss:
2, 2, 1, 2, 1, 2
2, 2, 1, 2, 2, 1
1, 2, 2, 1, 2, 2
2, 1, 2, 1, 2, 2
2, 2, 1, 1, 2, 2
2, 1, 2, 2, 1, 2
total: 26
wins: 6
therefore there are 6/26 ways BR could win
What I know is that there are 6 goals that have been scored in the game, and neither team scored three goals in a row. Below, I will write the Beaver Ranges (BR) and the Fox Raiders's (FR) goals. BR will be 1, and FR 2.
ReplyDeleteWins: (BR)
1, 1, 2, 2, 1, 1
1, 2, 1, 2, 1, 1
1, 1, 2, 1, 2, 1
1, 1, 2, 1, 1, 2
2, 1, 1, 2, 1, 1
1, 2, 1, 1, 2, 1
Ties:
2, 1, 1, 2, 1, 2
2, 1, 1, 2, 2, 1
2, 1, 2, 1, 1, 2
2, 2, 1, 1, 2, 1
2, 2, 1, 2, 1, 1
1, 2, 1, 1, 2, 2
1, 2, 1, 2, 1, 2
2, 1, 2, 2, 1, 1
1, 2, 1, 1, 2, 2
2, 1, 2, 2, 1, 1
1, 2, 1, 2, 2, 1
1, 2, 2, 1, 2, 1
Losses: (BR)
1, 2, 2, 1, 2, 2
2, 1, 2, 2, 1, 2
2, 1, 2, 1, 2, 2
2, 2, 1, 1, 2, 2
2, 2, 1, 2, 1, 2
2, 2, 1, 2, 2, 1
Shown above are the wins for BR, the losses for BR, and the ties. The total of all these possibilities is 26, and there are 6 of these possibilities where BR won. So therefore, there are 6/26 ways that BR could win.
Grade 7/8 POTW
ReplyDeleteIn order to solve this question, I decided to list all of the possibilities that met the criteria. (T means tie, 1 means Beaver rangers and 2 means Fox raiders)
1,1,2,1,1,2
1,2,1,1,2,1
1,2,1,2,1,1
1,1,2,1,2,1
2,1,1,2,1,1
1,1,2,2,1,1
Therefore, there are 6 ways that the Beaver Rangers could win.
1=BR 2=FR
ReplyDeleteWins:
1,1,2,1,1,2
1,2,1,1,2,1
1,2,1,2,1,1
1,1,2,1,2,1
2,1,1,2,1,1
1,1,2,2,1,1
Ties:
1,2,1,2,1,2
2,1,2,1,2,1
1,1,2,1,2,2
2,2,1,2,1,1
1,2,2,1,2,1
2,1,1,2,1,2
1,1,2,2,1,2
2,2,1,1,2,1
2,1,1,2,2,1
2,1,2,1,1,2
2,1,2,2,1,1
1,2,1,1,2,2
1,2,1,1,2,2
1,2,1,2,2,1
Losses:
2,2,1,2,2,1
2,1,2,2,1,2
2,1,2,1,2,2
2,2,1,2,1,2
1,2,2,1,2,2
2,2,1,1,2,2
There is a 6 in 26 chance that the Beaver Raiders will win. This is because there are 26 possibilities in total. 6 of which the Beaver Raiders have the probability to win. This is then a ratio of 6 to 26 or 6 in 26 chance.
Maxwell's Grade 8 POTW:
ReplyDelete1,1,2,1,1,2
1,2,1,1,2,1
1,2,1,2,1,1
1,1,2,1,2,1
2,1,1,2,1,1
1,1,2,2,1,1
Here are all the possibilities of the Beaver Rangers winning. This means that there are 6 ways that the Beaver Rangers can win.
GRADE 7/8 POTW:
ReplyDeleterelevant data -
1. beaver rangers won
2. no team scored 3 in a row
from that we can deduct that beaver rangers scored 4 goals as they can only win with 4+ goals out of the 6 as well as the fact that if it was 5 or 6 goals, they'd have to consecutively score 3. Now we will line up possible ways. (BR = beaver rangers, FR = fox raiders)
FR, BR, BR, FR, BR, BR
BR, BR, FR, BR, BR, FR
BR, BR, FR, FR, BR, BR
BR, FR, BR, BR, FR, BR
BR, FR, BR, FR, BR, BR
BR, BR, FR, BR, FR, BR
There are 6 ways for BR to win
Esther POTW
ReplyDeleteFirst I gathered the information that I will need:
Beaver Rangers won.
No teams scored 3 points in a row at any point.
6 points were scored in total.
Then I found out what I have to get out of this:
All possible final scores.
How each score was obtained.
I know that the only way the Beaver Rangers can win is if they score 4 or more points. This is true since half of 6 is 3 and that would be a tie. So the Beaver Rangers must score more than 3 points (half).
So then I listed the possible ways the Beaver Rangers could have won.
Beaver Rangers = A
Fox Raiders = B
A, A, B, A, B, A
A, B, A, A, B, A
A, B, A, B, A, A
A, A, B, A, A, B
A, A, B, B, A, A
B, A, A, B, A, A
There are 6 different possible ways that the Beaver Rangers could have won.
Info:
ReplyDeleteBeaver Rangers won the game of 6 points scored in total, where nobody scored 3 consecutive points at a time.
In order to win a game with 6 points scored, you have to have majority of those points. So, at least 4 points were scored by the Beaver Rangers.
Here are the possible orders that they could have won.
- BR, BR, FR, BR, FR, BR
- BR, FR, BR, BR, FR, BR
- BR, FR, BR, FR, BR, BR
- BR, BR, FR, BR, BR, FR
- BR, BR, FR, FR, BR, BR
- FR, BR, BR, FR, BR, FR
The Beaver Rangers could have won in 6 different ways.
The only possible score is 4 - 2
ReplyDeletepossible ways are as follows
BR = 2 FR= 1
1. 2,1,2,1,2,2
2. 2,2,1,2,1,2
3. 2,1,2,2,1,2
4. 1,2,2,1,2,2
5. 2,2,1,2,2,1
6. 2,2,1,1,2,2
There are 6 possible bays for the Beaver rangers to win.
POTW:
ReplyDeleteFirst off, we can eliminate 6-0 because that would mean the beaver rangers had to score more than 3 times in a row. We can also eliminate 5-1 because that would mean the beavers scored three time in a row. So now we only have 4-2, and this makes sense and so all the possible combinations that the Beaver Rangers won:
BR, FR, BR, BR, FR, BR
BR, BR, FR, BR, BR, FR
BR, FR, BR, FR, BR, BR
BR, BR, FR, BR, FR, BR
BR, BR, FR, FR, BR, BR
FR, BR, BR, FR, BR, FR
The different possibilities of the Beaver Rangers winning is 6. (While following the rules)
POTW #7:
ReplyDeleteThere were six points in total during the game.
To make the Beaver Rangers win the game, In the patterns of the scores, Beaver Rangers have to appear 4 times and Fox Raider 2.
Also, The Beaver Rangers had to win and no one scored three times in a row.
BR: Beaver Rangers
FR: Fox Raiders
To find the patterns, I just listed the teams in a random order and followed the requirements needed for the Beaver Rangers to win.
1. BR, FR, BR, FR, BR, BR
2. FR, BR, BR, FR, BR, BR
3. BR, BR, FR, BR, BR, FR
4. BR, FR, BR, BR, FR, BR
5. BR, BR, FR, FR, BR, BR
6. BR, BR, FR, BR, FR ,BR
In the soccer game, The Beaver Rangers have 6 possible ways they could have won.
For this question I decided to list out all of the possibilities:
ReplyDeleteWinning scores for the Beavers:
1) BR, BR, FR, BR, FR, BR
2) BR, FR, BR, BR, FR, BR
3) BR, FR, BR, FR, BR, BR
4) BR, BR, FR, BR, BR, FR
5) BR, BR, FR, FR, BR, BR
6) FR, BR, BR, FR, BR, FR
Therefore, there are 6 ways that the Beaver Rangers could have beat the Fox Raiders.
There are 6 ways either team could pull ahead and win.
ReplyDeletePOTW:
ReplyDeleteThere are six different possible ways that the Beaver Rangers could have beat the Fox Raiders
BR= Beaver Rangers
FR= Fox Raiders
1. BR,BR,FR,BR,FR,BR
2.BR,BR,FR,BR,BR,FR
3. BR,FR,BR,FR,BR,BR
4. BR,BR,FR,FR,BR,FR
5. FR,BR,BR,FR,BR,BR
6. BR,FR,BR,BR,FR,BR
The Beaver Rangers needed to score 4 points to win, and I just listed out all the possibilities (B= Beaver Rangers, F = Fox Raiders):
ReplyDelete- B, B, F, F, B, B
- B, B, F, B, B, F
- B, B, F, B, F, B
- B, F, B, F, B, B
- B, F, B, B, F, B
- F, B, B, F, B, B
There are 6 possibilities for the Beaver Rangers' win.
The Beaver Rangers needed to score 4 points to win, and I just listed out all the possibilities (B= Beaver Rangers, F = Fox Raiders):
ReplyDelete- B, B, F, F, B, B
- B, B, F, B, B, F
- B, B, F, B, F, B
- B, F, B, F, B, B
- B, F, B, B, F, B
- F, B, B, F, B, B
There are 6 possibilities for the Beaver Rangers' win.
B=Beavers
ReplyDeleteF=Fox
BBFBBF
FBBFBB
BFBFBB
BBFBFB
BFBBFB
BBFFBB
FBBFBB
The beavers must score 4 points in order to make the score in their favor but 5 goals can not be scored due to the fact that the team never scored 3 goals in a row.I counted 6 possibilities in total.
Since Beaver Rangers must win, they have to score 4 goals
ReplyDeleteB,B,F,B,B,F
B,B,F,F,B,B
B,B,F,B,F,B
B,F,B,B,F,B
B,F,F,B,B,B
F,B,B,F,B,B
There are 6 ways for BR to win
Grade 7/8 POTW #6
ReplyDeleteThere is a total of 26 possibilities. Out of those 26, the Beaver Rangers can win 6 (6/26).
The 6 possible ways for the Beaver Rangers to win are: (BR = 1 FX = 2)
1,1,2,1,1,2
1,2,1,1,2,1
2,1,1,2,1,1
1,1,2,1,2,1
1,1,2,2,1,1
1,2,1,2,1,1