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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

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.

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:

1. Total horses including the neighbor’s horse: 17 + 1 = 18 horses.
2. 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:

$17$

3. 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.

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.

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

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.