POTW 28 Gr. 7 Question:
POTW 28 Gr. 8 Question:
POTW 27 Gr. 8 Solution:
POTW 27 Gr. 7 Solution:
Thursday, April 27, 2017
POTW #28 - Logically Logical
Welcome back to another POTW. Use your logic skills and your riddle skills (think Einstein's riddle we did) to solve the latest POTW below...but don't forget to first review the POTW 27 solution!
POTW 28 Gr. 7 Question:
POTW 28 Gr. 8 Question:
POTW 27 Gr. 8 Solution:
POTW 27 Gr. 7 Solution:
POTW 28 Gr. 7 Question:
POTW 28 Gr. 8 Question:
POTW 27 Gr. 8 Solution:
POTW 27 Gr. 7 Solution:
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Grade 7 POTW:
ReplyDeleteHow I did it was to logically determine the number of Nanos and Technos.
Since one condition is that one Nano is the same height of a Techno, that would mean that it would be 157 cm because if it was 153, the other condition states that two Nanos would be the same height. This height would be 157, which is impossible since no Nano is taller than one Techno, one being 153.
Therefore, the height of the Nano and Techno is 157 cm.
All the other heights of the students that are lower than 157 cm are Nanos.
These would be 151,153,153,154, 156, and 157.
The Techno heights would be 157, 159, and 161 cm.
Now, I would need to find the mean of these two lengths.
157+159+161 = 477
477/3 = 159. This is the mean of the technos.
The other lengths add up to 924.
Divided by 6, it would be 154. This is the mean height of the Nanos.
The mean of this is (159+154)/2= 156.5.
The mean is 156.5 cm.
-Alan
Oops I just realized I did the question wrong! The last part is incorrect. Subtract 159 by 154 to give 5 as the difference.
Delete-Alan
Grade 8 POTW:
ReplyDeleteFirst step is to find the easiest part to solve.
Looking at the chart, I can see that Deanna has no one taller than her in the front or in the back. This would prove that she is the tallest, since no matter where she is placed in the line, if there was someone in the line taller than her, then it would be stated in the chart. Since it was not stated, Deanna is the tallest person.
Ceilidh has only one person taller than her in the front, which would be Deanna. Nobody else is taller than her in the back, which would prove that she is the second tallest.
Eartha has two people taller than her, being Ceilidh and Deanna. That means that she is third tallest.
Using this logic, I can also prove that Avery is fourth tallest, while Bethany is the shortest.
The order would be Deanna, Ceilidh, Eartha, Avery, and Bethany.
Now, we would have to figure out what the lineup is. Let's start with Bethany.
Because she has three in front and 1 behind, this would make her fourth in line.
Avery has 1 person in front taller than him and two behind him. This would make him in front of Bethany, but we do not know where. Using logic, I can see that since there is one person taller than him in front of him, he only has two possibilities: Second in line or third in line. Now, he cannot be third in line because he is the second shortest, and if he was put third in line then there would be two people in front of him that is taller than him, which from the chart is false. Therefore, he is second in line.
Eartha has two people taller than her in front. Because there are only three possible spaces, she must be in the very back so that the other two spaces are filled with Ceilidh and Deanna, who are both taller than her.
Ceilidh has one person in front of her that is taller than her, who would be Deanna.
Deanna is then the most front.
So, the order in the line from back to front is:
Eartha, Bethany, Ceilidh, Avery, and Deanna.
-Alan
Gr. 7 POTW, we know one of the nanos and one of the technos is 157 since if the first condition was 153, then the two nanos that are the same height, is 157 but that would mean the nano is taller than the techno. With this, we can determine that
ReplyDeleteThe Nanos: 151, 153, 153, 154, 156, 157
The Technos: 157, 159, 161
Mean:
151+153+153+154+156+157=
924/6=
154
The mean for the nanos' height is 154cm
157+159+161=477
477/3=159
159-154=5
The mean difference is 5cm.
Maxwell and Avi's Grade 7 POTW:
ReplyDeleteSo the mean for the Nanos is 154 cm. The mean for the Technos is 159 cm. That means that the difference of the two means is 5 cm.
Nano Heights:
ReplyDelete151, 153, 153, 154, 156, 157
Techno Heights:
157, 159, 161
Finding Average/Mean:
Nanos:
151 + 153 + 153 + 154 + 156 + 157 = 924
924/6 = 154
The average height of the Nanos is 154 cm.
Technos:
157 + 159 + 161 = 477
477/3 = 159
The average height of the Technos is 159 cm.
Final Result:
159 - 154 = 5
Therefore, the difference between the two means is 5 cm.
Here is how I solved it:
ReplyDeleteSo first I made a graph to determine the positions of everyone:
Each letter represents the person with that letter being the first of their name ( e.x. Avery is represented as "A")
5th 4th 3rd 2nd 1st
A A A A A
B B B B B
C C C C C
D D D D D
E E E E E
It is possible for them to be anything. So I analysed the graph, from what I saw, Deanna is the tallest and Bethany is the shortest. The graph shows that There is one person who is taller behind Bethany and three people who are taller in front, this means that Bethany is 4th in the line.
5th 4th 3rd 2nd 1st
A A A A
B
C C C C
D D D D
E E E E
Next, it says that there are two people taller than Avery behind her and one person taller than her in front. This means she is the fourth shortest. The only possible position for her is to be 2nd in the line.
5th 4th 3rd 2nd 1st
A
B
C C C
D D D
E E E
Next, Eartha says that there are two people taller than are in front, but no one is taller than her behind her. considering that Bethany and Avery are 4th and 2nd respectively, the only position Eartha can be in is 5th.
5th 4th 3rd 2nd 1st
A
B
C C
D D
E
The graph then says that there is no one taller than Celidh behind her, but someone in front is. This means that Celidh is in the middle.
5th 4th 3rd 2nd 1st
A
B
C
D
E
With all other spots taken, that means Deanna is first.
The order from tallest to shortest is: Deanna, Celidh, Eartha, Avery, and then Bethany.
Michelle Grade 7 POTW:
ReplyDeleteThe difference between the 2 averages is 5.
Nano: 151, 153, 156, 157, 154, 153 heights
Mean: 154 cm
Techno: 157, 159, 161
Mean: 159 cm
159 cm - 154 cm = 5 cm <---- difference
Rest of the work is in my book.
-m
Nanos Heights: 151, 153, 153, 154, 156, 157
ReplyDeleteTechno Heights: 157, 159, 161
These are the number I got. These numbers fit the criteria exactly, because no nano is taller than a techno and 2 nanos are the same. Also 1 nano is the same height as one techno.
Now I just need to find the difference between averages.
NANOS
151 + 153 + 153 + 154 + 156 + 157 = 924
924 / 6 = 154
TECHNOS
157 + 159 + 161 = 477
477 / 3 = 159
Using the information above I can now see that the Technos mean height is 159cm and that the Nanos mean height is 154. This means that the difference between the two mean heights is 5cm.
Grade 7 POTW:
ReplyDeleteSince the Nanos all have smaller heights than the Technos (except for one), the Nanos are the people with the shortest heights up to 157cm (The height of a Nano/Techno), and the Technos are the people with heights from 157cm. Using this information, I made a list of the heights of Nanos/Technos.
Nano Heights: 151cm, 153cm, 153cm, 154cm, 156cm, 157cm
Techno Heights: 157cm, 159cm, 161cm
Using this information, we can figure out the means of the Nano/Techno heights, which are 154cm and 159cm respectively. Since 159-154 is 5, there is a 5cm difference between the mean heights of the Nanos and Technos.