Latest Logic Riddles

To keep odds in his favor, Alpha must choose a card from the first three whenever he sees a 9 or higher card.

This is because the probability that all cards that are selected randomly by beta are below 9 is 32*231*30*29 / 52*51*50*49 = 0.133.
In such a case, you lose from $2 to $9 with equal probability = 0.133/8 = 0.0166

Let us now calculate the probability of the four cards being of value 9 or higher which will be equal to 1 – 0.133 = 0.867.

As Alpha stops at the first sight of 9 or a higher card, he can possibly win -1, 0, 1, 2, 3 with an equal probability of 0.867/5 = 0.173

This will give him an overall expected winning amount of 0.14 per game he plays.

Also note that if Alpha decides to stop at a card 10 or higher, the expected winning amount will be 0.09 per game. It can be a strategy to win more but will not stand quite effective.

With any other choice of stopping, Alpha will be having negative chances of winning.

Robin Stole Cat
Steve stole Hen
Tim Stole Dog

Glance at the first and second statement again; they are contradictory. Both can be true together though. Also both of them cannot be false which means that Tim stole cat and his statement will be true. But it has been already deduced that the one who stole cat was telling a lie thus it can’t be possible.

Let us consider the situation again. It may be that Tim stole a hen or a dog. Assume that he stole hen. In such a case the statement of Tim will be false. But we know that the person who stole hen told the truth, thus it is contradicting our assumption and so cannot be correct.

Considering everything, now we can say with confidence that Tim stole the dog.

Now it means that the statement by Robin is completely false and the statement by Steve is true which depicts that the cat and hen are stolen by these two. Also we know that the one who stole hen is true and the one stealing cat is a liar. Thus we now know that Robin stole cat and Steve stole hen.

D
C
A
B

I spoke with Mia.

Let us assume that Tia is a liar and Mia is a truth teller.
If I asked the question from Mia, the answer will be yes. If I asked the question from Tia, the answer will be no. Thus I must have asked from Mia.

Let us assume that Tia is a truth teller and Mia is a liar.
If I asked the question from Mia, the answer will be yes. If I asked from Tia, the answer will be no. Thus in this case as well, I must have asked from Mia.

45minutes

It is not as hard as it seems. I will burn one wire on both ends and the other wire at one end only. The first wire will burn completely in thirty minutes and at that very moment, I will burn the other end of the second wire and it will burn in fifteen minutes. Thus both of the wires will be burnt in 30 + 15 = 45 minutes.

Let us consider the length of the tunnel first; which is 200 miles. Now, the trains are running on the same speed which means that they will collide at the center of the tunnel and will take an hour to reach the center. Now the bird is travelling at a speed of 1000 mph and it is flying for an hour (since the trains will take an hour to collide). Thus the bird will travel 1000 miles in the process.

The answer is 456,789.

Let us begin with two residents. The number of hairs on their head can be zero and one. If we extrapolate the fact, we will come to know that the number of hairs with 'n' number of residents will always range from zero to (n-1).

If we go above 456,789 to 456,790 with none of the residents having 456,789 hairs, the number of hairs on them will be different and one of them must have more than 456,789 which will clearly violate the fact that the number of residents are more than hairs on an individual.

Mr. Bilbo did it.

Let us consider all the statements one by one for every person and find out.

Case 1: Mr. Bilbo did it, then
Statement 1 => true
Statement 2 => false (as Reese did not do it)
Statement 3 => false (as Mr. Bilbo is lying)
Statement 4 => false (as Mr. Gerry is lying)
It was Mr. Bilbo who did it. But let us confirm by taking up other cases as well.

Case 2: Mr. Reese did it, then
Statement 1 => false (as Mr. Bilbo did not do it)
Statement 2 => true
Statement 3 => true (as Mr. Bilbo is not lying)
Two statements are true whereas only one should be true, thus Mr. Reese did not do it.

Case 3: Mr. Gerry did it, then
Statement 1 => false (as Mr. Bilbo did not do it)
Statement 2 => false (as Mr. Reese did not do it)
Statement 3 => false (as Mr. Bilbo is lying)
Statement 4 => false (as Mr. Gerry is lying)
All four statements stand false, thus Mr. Gerry did not do it.

Case 4: Mr. Yang did it, then
Statement 1 => false (as Mr. Bilbo did not do it)
Statement 2 => false (as Mr. Reese did not do it)
Statement 3 => false (as Mr. Bilbo is lying)
Statement 4 => false (as Mr. Gerry is lying)


All four statements are false therefore Mr. Yang did not do it.

We have verified with everyone and now know that it was Mr. Bilbo who did it.

The Password, Clues 2 and 5 are correct and rest are lies.

Ponder over the bulb number 56, people will visit it for every divisor it has. So 56 has 1 & 56, 2 & 28, 4 & 14, 7 & 8. So on pass 1, the 1st person will light the bulb; pass 2, 2nd one will switch it off; pass 4, light it; pass 7, switch it off; pass 8, light it; pass 14, switch it off; pass 28, light it; pass 56, switch it off.
For each pair of divisors the bulb will just end up back in its preliminary state. But there are cases in which the pair of divisor has similar number for example bulb number 16. 16 has the divisors 1 & 16, 2 & 8, 4&4. But 4 is recurring because 16 is a perfect square, so you will only visit bulb number 16, on pass 1, 2, 4, 8 and 16… leaving it lit at the end. So only perfect square bulbs will be lit at the end.