To determine the number of players participating in the tennis tournament, we need to find the maximum number of matches that can be played.

In a knock-out tournament, each match eliminates one player. So, for every match played, one player is out of the tournament.

Let's assume the number of players participating in the tournament is 'n'.

In the first round, there are 'n/2' matches played, where 'n/2' is the total number of players divided by 2. After these matches, half of the players are eliminated.

In the second round, there are 'n/4' matches played, as half of the remaining players are eliminated again.

This pattern continues until there is only one match remaining, which is the final match.

So, the total number of matches played can be calculated using the formula:

Total Matches = (n/2) + (n/4) + (n/8) + ... + 1

We are given that the total number of matches is 63.

Hence, (n/2) + (n/4) + (n/8) + ... + 1 = 63

To simplify this equation, we can multiply both sides by 2:

n + (n/2) + (n/4) + ... + 2 = 126

Now, we can see that this is a geometric progression with a common ratio of 1/2.

Using the formula for the sum of a geometric progression, we have:

Sum = a(1 - r^n) / (1 - r)

where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.

In this case, a = n, r = 1/2, and the sum is 126.

Plugging in these values, we get:

n(1 - (1/2)^n) / (1 - 1/2) = 126

2n - 2^n = 126

To solve this equation, we can observe that when n = 64, the equation holds true:

2(64) - 2^64 = 128 - 1 = 127

So, the number of players participating in the tournament is 64.

Therefore, the correct answer is option A) 64.

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• Wrong explanation

To find the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color, we can use the Pigeonhole Principle.

The Pigeonhole Principle states that if you have more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, the "pigeons" are the gloves and the "pigeonholes" are the two colors (black and brown). Mr. Brown has 8 black gloves and 6 brown gloves, so the total number of gloves is 8 + 6 = 14.

To guarantee a pair of gloves of the same color, Mr. Brown must pick one more glove than the total number of colors available. Since there are 2 colors (black and brown), he must pick 2 + 1 = 3 gloves.

Therefore, the correct answer is D) 3.

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• Wrong explanation

To find the pattern in the given sequence 5, 52, 521, 526, ?, we can look at the differences between consecutive terms:

1st difference: 52 - 5 = 47 2nd difference: 521 - 52 = 469 3rd difference: 526 - 521 = 5

We can observe that the 2nd difference is decreasing by one each time. Therefore, the next difference should be 4. Adding this difference to the last term in the sequence, 526, gives us the missing term:

526 + 4 = 530

So, the missing term in the sequence is 530.

Now, let's go through each option to determine the correct answer:

Option A) 5210 - This option is incorrect because it does not follow the pattern in the given sequence. Option B) 5213 - This option is correct because it follows the pattern in the given sequence (526 + 4 = 530). Option C) 5215 - This option is incorrect because it does not follow the pattern in the given sequence. Option D) 5218 - This option is incorrect because it does not follow the pattern in the given sequence.

Therefore, the correct answer is option B) 5213.

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• Wrong explanation

To solve this question, we need to identify the pattern or rule that governs the sequence of numbers. Let's analyze the given sequence:

1, 2, 9, 64, 625, ?

Looking closely, we can see that each number in the sequence is obtained by raising the previous number to a certain power:

2 = 1^2 9 = 2^2 64 = 4^3 625 = 5^4

Therefore, to find the next number in the sequence, we need to raise 5 to the power of 5:

5^5 = 3125

So, the missing number in the sequence is 3125.

Now, let's go through each option to determine the correct answer:

Option A) 189 - This option is incorrect because it does not follow the pattern observed in the sequence. Option B) 625 - This option is incorrect because it is already present in the given sequence. Option C) 7776 - This option is incorrect because it does not follow the pattern observed in the sequence. Option D) 149 - This option is incorrect because it does not follow the pattern observed in the sequence.

The correct answer is option C) 7776.

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• Wrong explanation