The key to understanding the paradox is to consider the probability of each possible outcome before the second ball is drawn.

At the beginning, when all four balls are in the hat, the probability of drawing the white ball is 1/4, the probability of drawing the blue ball is 1/4, and the probability of drawing one of the red balls is 2/4 or 1/2.

When the first ball is drawn and revealed to be red, the probability of the remaining balls in the hat changes. There are now three balls left, one white, one blue, and one red. The probability of drawing the white or blue ball is 1/3 each, and the probability of drawing the remaining red ball is 1/3 as well.

Given that at least one of the balls drawn is red, we know that the red-red outcome is possible, and so is either the red-blue or red-white outcome.

Therefore, the probability that the second ball drawn is also red is the probability of the red-red outcome divided by the probability of the two possible outcomes that include at least one red ball, which is 1/2. So the probability of the second ball being red is 1/2, or 50%, which is different from what intuition might suggest.

2*(2+3)-2=8
3*(3+7)-3=27
4*(4+5)-4=32
5*(5+8)-5=60
7*(7+8)-7=98

Chile (pronounced “chill-ay”) – as in the verb “to chill,” meaning to make someone feel cold or cause a shiver, and also a reference to the South American country of Chile.

7th is Lampard and the 8th is Torres.
If we consider the statement “X of us are lying here” as “Exactly X of us are lying here” and there are only one player named Lampard and one player named Torres than statement (1) can be true so statements (7),(8) are false and therefore the person saying he is Torres is actually Lampard  and vise versa.

Now lets see another approach:
Since statements (3) and (4) are the same than they both can be true or both false. So if they are both true that leaves only one more statements as true and since no other statement of the form: “X of us are lying here” can be true than means than only one of the statements  (7), (8) is true and that is not an option so that means that statements (3) and (4) are False.
We know that statements (7), (8) can also both be true or both false.
If they are true than the options are :
>>>>  6 are lying > it contradicts with statement (2)
>>>>  5 are lying > it contradicts with statements (3) and (4)
>>>>  4,3 are lying means there are 2,3 more true statements but statements (1),(2),(5),(6) contradict between themselves so the only solution is that (7) and (8) are false and (1) is true.

Lets  say that the speed of me is V1 and my friend speed is V2.  Since we both arrived  at the same times, means that it took him to path the distance that I walked for 4:05 hours (4+1/12=49/12) the same time as it took me to path the distance he walked for 2:05 hours (2+1/12=25/12)

so we can write: 49 * V1          25 *  V2
                                      ———-  =   ———-   >>>     49 * V1^2  = 25 * V2 ^2  >>>>   7 * V1  =  5 *  V2 >>>  V1 = (5/7) *V2
                                      12 * V2          12 *   V1

So now we can calculate the time after the meeting:  (49/12) * [(5/7)*V2]/V2 = 35/12 = 2+11/12 = 2:55.  So since the meeting  was at 4:05 they we both arrived at 4:05+2:55=07:00 pm

You can’t divide by zero!! In the equation A(A-2) = A-2 you can not divide both sides by (A-2) to get A =1 since A=2 and A-2 is zero.

Let the three consecutive numbers be x, x+1, and x+2.

When we divide the product of these three numbers by the first number x, we get: (x)(x+1)(x+2)/x = (x+1)(x+2)
When we divide the product by the second number x+1, we get: (x)(x+1)(x+2)/(x+1) = (x)(x+2)/(x+1)
When we divide the product by the third number x+2, we get: (x)(x+1)(x+2)/(x+2) = (x)(x+1)
According to the problem, the sum of these three quotients is 74, so we can write the equation:
(x+1)(x+2) + (x)(x+2)/(x+1) + (x)(x+1) = 74
Expanding the terms and simplifying, we get:
3x^2 + 6x – 72 = 0

Dividing by 3 and factoring, we get:  x^2 + 2x – 24 = 0
(x+6)(x-4) = 0

So x = -6 or x = 4. Since the numbers are consecutive, x must be positive, so x = 4.

Therefore, the three consecutive numbers are 4, 5, and 6.

The answer to this riddle is “charcoal.”

When charcoal is bought, it is black in color, as it is made from carbon-rich materials like wood or coconut shells that are heated in the absence of air.

When charcoal is used, it turns red when it is lit and burns.

When charcoal has been used up, it turns into gray ash, which is what is left when the carbon in the charcoal has been fully burned away. This gray ash can then be thrown away.

A hole

Answer: 52 comparisons which is also the worst case

Here’s how the algorithm works:

1. Divide the 38 numbers into pairs, and find the smallest number in each pair. This takes 19 comparisons.
2. Take the 19 smallest numbers and pair them up again, finding the smallest number in each pair. This takes 18 comparisons.
3. Take the 9 smallest numbers and pair them up again, finding the smallest number in each pair. This takes 8 comparisons.
4. Take the 5 smallest numbers and pair them up again, finding the smallest number in each pair. This takes 4 comparisons.
5. Take the 3 smallest numbers and pair them up again, finding the smallest number in each pair. This takes 2 comparisons.
6. Take the 2 remaining numbers and find the smallest one. This takes 1 comparison.

Adding up the comparisons from each step gives us a total of 19+18+8+4+2+1=52 comparisons. However, in the worst case scenario, the two smallest numbers are always paired up in the last step.