Logic Riddles

Answer: 9 minutes.

Each path has an equal chance of occurring and if B or D are chosen they will just add 8 or 2 minutes to the time because the rat must restart the maze: time = (1/4)*5 + (1/4)*(8 + time) + (1/4)*(3) + (1/4)*(2 + time). Time = 9 minutes.

Answer: 7 races are required.

First you divide the 25 horses into 5 groups of 5. You conduct the 5 races and take all of the fastest horses in those races and have a race with them, giving you the fastest horse. Then you take the remaining 24 horses (excluding the fastest) and remove the 4th and 5th horses in the first set of 5 races (since they definitely have 3 horses faster than them), leaving you with 14 horses. Next you can remove all of the horses that were beat in the preliminary race by the horses that got 4th and 5th in the championship race, leaving you with 8 horses. Finally, you can remove the horses that remain that lost to the 3rd place horse in the final race in the preliminary race and the horse that got 3rd in the preliminary to the horse that got 2nd in the championship race, leaving you with 5 horses.

You can then run a final race where the 1st and 2nd place horses are the 2nd and 3rd fastest. Then you know the 3 fastest horses.

Answer: No. When you remove the two diagonal spaces from the chess board they are both black or both white, making it so that there are two more of the other color. Each domino would cover 1 black and 1 white space. So 31 of them would have to cover 31 white spaces and 31 black spaces but with the corners removed there are 30 of one color and 32 of the other.

Answer: 90 percent. If you pick the heads coin the chance of getting the first 2 heads is 100 percent (4/4) and if you pick the fair coin the chance is 25 percent (1/4). So from this, the chance that it is the heads coin is 4/5 and the fair coin 1/5.

Then, if it is the heads coin you will definitely get heads (4/5). If you flip the fair coin it is 1/10 (1/5 * 1/2). Add the probabilities together: 4/5 + 1/10 = 9/10.

Answer: It moves forward towards the front of the car, even though you are forced backwards. The helium balloon is less dense than the air so when you accelerate the air in the car will move backwards compared to the balloon pushing the balloon forward because the balloon is lighter.