Puzzle Cow

Question 1: Are you the truth teller?

Question 2: (a) If the person responds "Yes". They are either the truth teller or they are a toggler that has just lied to you that will now tell you the truth. Either way the next answer will be truthful. Therefore ask who is the truth teller.

Question 2 (b) if the answer to question 1 is "no". They have to be a toggler that has just told you the truth. Therefore the next question will be a lie. Therefore the question " who is a toggler" will reveal the truth teller.

The math at the end of the question makes you add up numbers wrong
The Men started with $30
They were returned $1 each so they payed $27.
The restaurant took $25
The waiter took the last $2
$30-$3 = $27 ( $25 to restaurant, $2 to the waiter)

My father's son is yourself. Therefore. That man's father is yourself. Therefore it is your son.

Technique:
Once you've reached halfway, if you see a card that's higher than all the other cards, tell the dealer to stop. If you take note of the second highest card in the first half of the deck. and then pick any card higher than the this card in the second half of the deck you will have a 1/4 chance of selecting the highest card.

Explanation:
There is a 1/2 chance that the second highest card is in the first half of the deck. There is a 1/2 chance that the highest card is in the second half of the deck. Therefore there is a (1/2)*(1/2) = 1/4 chance that both these conditions hold true. If both these conditions hold true you will always pick out the highest card. Amazingly the outcome has nothing to do with the size of the deck!

Divide the coins into three groups of 9 and put 2 of the groups on either end the scale. If they weight the same amount, it means the counterfeit coin is in the pile not on the scale. Of course if one side goes up the counterfeit coin is in that stack of 9. Now take that stack of 9 and divide evenly again into stacks 3 groups of three and put two of groups of the scale. Use the same technique. You will find a group of 3 be left with a group of 3 coins. Now weigh two of those coins and voila. The counterfeit coin!

Let P represent the pirates.
If 1 pirate were left 'P5' receives all the gold.
If 2 pirates were left 'P5' would vote against 'P4', thus killing 'P4'. 'P5' knows that if he votes against 'P4', next round he will receive all the gold.
P4 = 0gold P5 = 100gold

If 3 Pirates were left. 'P3' knows that if it gets down to 2 pirates, 'P4' is a dead man. Therefore he knows 'P4' will vote for him not matter what therefore he can keep all the gold himself. And stay alive with a vote from 'P4'
P3= 100 gold P4=0 gold P5= 0 gold

With 4 pirates left. 'P4' needs 2 votes to stay alive. By giving 'P2' and 'P1' 1 gold each, they are guaranteed more than if it goes another round.
P2=98 P3=0 P4=1 P5=1

With 5 pirates left. 'P5' (you) needs 2 more votes. Giving 'P4' 2 gold and 'P3' 1 gold will guarantee your survival.
P1=97 P2=0 P3=1 P4=2 P5=0
Or
P1=97 p2=0 p3=1 p4=0 p5=2
Therefore you can safely keep 97 gold.

Light both ends of rope 'A'. At the same time light one end of rope 'B'. Once rope A has burnt out light the remaining end of rope 'B'.

Yes a married person is looking at a non-married person. Martha is either married or not married. If Martha is not married then Jane(married) is looking at Martha(not married. If Martha is married then Martha(married) is looking at Jane(not Married).