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PBL Q11

Perimeter = 25 + 25 + 10 + 10 + 5 + 5 = 80

Answer for question 3

When four cars have traveled ¼ of the total distance, there is sufficient fuel to fill two full tanks. After traveling another ¼ of the total distance, there is enough fuel to fill one full tank. Finally, the remaining car will have enough fuel to reach their destination.

The previous response only partially answers the question. To get full mark, the answer is three cars.

We start with 3 cars, all with full tanks. Car 3 keeps the parcel.

All 3 cars travel 1/6 of the total distance.
At that point, Car 1 and Car 2 each transfer of their tanks to Car 3. Now Car 3 has a full tank, and Car 1 and Car 2 still have 1 -(1/3) -(1/6) = 3/6 of a tank each that is enough to get back to the start to refuel.
Car 3 travels 1/6 forward of the total distance and has 2/3 of a tank.
Car 1 and Car 2 start again from the beginning with full tanks and travel forward again to 1/6 of the total distance.
At that point, Car 1 transfers of the tank to Car 2 to make Car 2 has a full tank.
Car 2 travels 1/6 forward of the total distance and meet Car 3. Both Car 2 and Car 3 has 2/3 of a tank.
Now Car 1 has 1/3 of a full tank that is enough to get back to the start to refuel.
Car 1 starts again from the beginning with full tanks and travel forward to 2/6 of the total distance to meet Car 2 and Car 3.
At this point, Car 1 transfers its remaining of the tank to Car 3 and cannot move any more. Car 3 has a full tank now.
Car 2 and Car3 travel 1/6 further to the middle of the total distance. At this point, Car 2 has 1/3 of a tank and Car 3 has 2/3 of a tank. Car 2 transfers its remaining of the tank to Car 3 and cannot move any more.
Car 3 has full tank at the 3/6 of the total distance and can make it all the way across the desert.

Answer for question 7

Borrow a horse from the neighbor and make the total number of horses to 18. This allowed the horses to be divided easily according to the father’s wishes. Here’s how it works:

Total horses including the neighbor’s horse: 17 + 1 = 18 horses.
Divide the horses according to the father’s will:
- Eldest son: 1/2 of 18 = 9 horses.
- Second son: 1/3 of 18 = 6 horses.
- Youngest son: 1/9 of 18 = 2 horses.

Adding these up:

$17$

The neighbor then takes his horse back, leaving the sons with the correct number of horses as per their father’s will, and no horses were sold or killed.

Answer for question 10

Answer for question 9

Let x be the number of correct answer

Let y be the number of wrong answer

8x-5y = 0

x+y=26

13x=130

x=10

y=16

Answer for question 8

Start both the 7-minute hourglass and the 11-minute hourglass at the same time. Once the 7-minute hourglass finishes its cycle, start a timer. After 4 minutes have passed, invert the 11-minute hourglass when it completes its first cycle. When the 11-minute hourglass finishes another full 11-minute cycle, the total elapsed time will be the initial 4 minutes from the inversion of the 11-minute hourglass, added with the 11 minutes of its second cycle, resulting in a total of 15 minutes.

Answer for question 6

Try thinking beyond conventional boundaries or norms. The significance of the numbers in this sequence extends beyond their numerical value. Instead, they represent the length of each word in the sequence, starting with the number one. The sequence is as follows: 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6. The last number, 6, corresponds to the word “twelve,” which consists of six letters. Consequently, the subsequent three numbers, 8, 8, and 7, illustrate the number of letters in the words “thirteen,” “fourteen,” and “fifteen,” respectively.

Answer for question 5

The sequence follows the pattern: 1, 2, 2, 4, 5, 9, 13, 22, 34, 56, …
Starting from the third number, each subsequent number is obtained by summing the previous number with either -0 or -1, depending on its position in the sequence. If the position is odd, subtract 1; if the position is even, subtract 0. For instance, in the third position, 1 + 2 – 1 = 2; in the sixth position, 4 + 5 – 0 = 9. Therefore, the next three numbers are calculated as follows:
34 + 56 – 1 = 89
56 + 89 – 0 = 145
89 + 145 – 1 = 233

Answer for question 4

Let’s engage in critical thinking. When Alice is asked if she is a truth teller, her response presents two potential scenarios: If Alice is a truth teller, she consistently speaks the truth, and thus she would answer with “Yes, I am a truth teller.” If Alice is a liar, she habitually tells lies, and therefore she would also respond with “Yes, I am a truth teller.”

Now, let’s analyze Bob’s statements. Bob claims, “Alice says yes,” suggesting that Bob is a truth teller. Additionally, Bob asserts that Alice is a liar.

Answer for Question2

Using the process of hypothesis and ruling out by contradiction, we can evaluate all different scenarios:

Scenario 1: Assume A is a liar.

D is the shortest.
A is either the 2nd or 3rd tallest since D is the shortest.
B is also either the 2nd or 3rd tallest.
C cannot be the shortest.
C is the tallest as A and B are 2nd or 3rd tallest.
This hypothesis is consistent and viable.

Scenario 2: Assume B is a liar.

A is the tallest.
B can be either the tallest or shortest, but A is the tallest, B must be shortest.
However D is already established as the shortest.
This contradicts the scenario, rendering it invalid.

Scenario 3: Assume C is a liar.

Both C and D being the shortest creates a contradiction.
Therefore, this hypothesis is not valid.

Scenario 4: Assume D is a liar.

A is the tallest.
B is the 2nd or 3rd tallest.
C and D can be either the tallest or 2nd or 3rd tallest.
As A is the tallest, C and D can be either 2nd or 3rd tallest.
It is impossible that three people B,C and D are 2nd or 3rd tallest at the same time
Thus, this hypothesis does not hold.

In conclusion, only Scenario 1 is valid, indicating that C is the tallest and D is the shortest.