A Sailor’s Bet

Yesterday’s Problem:

You participate in a virtual reality game in which you are given the chance to fight either one brontosaurus or three smaller stegosaurs in a row.

You know in advance that your chances of defeating the brontosaurus are one in seven, while the probability of defeating one of the stegosaurs is 1/2.

Which alternative should you choose? That is, which choice gives you the better chance of winning the game?

Answer:

Your better bet is to fight the brontosaurus. Although your chances of beating any stegosaur is 1/2. beating three in a series brings the probability down to 1/8: 1/2 * 1/2 * 1/2 = 1/8. Since the probability of beating the brontosaurus is higher (1/7), you are better off fight him, not the stegosaur.

Today’s Problem:

An old wartime story describes a sailor who, during a battle, put his head through a hole made in the side of his ship by an enemy shell. His theory was that the odds of another shell landing in exactly the same spot should be exceedingly small.

Was his reasoning correct?

The Virtual Reality Game

Last Problem:

Six men check their hats at the theater. An inattentive attendant mixes up the claim checks, so when the men return after the show the hats are essentially handed out at random.

If someone offered you even money to bet that at least one of the men got his own hat back, would you take the bet? In other words, do you believe that the probability of one of the six men getting his own hat back to be greater than .5?

Answer:

You should take the bet. The probability of at least one man getting his own hat back is almost .632.

Today’s Problem:

You participate in a virtual reality game in which you are given the chance to fight either one brontosaurus or three smaller stegosaurs in a row.

You know in advance that your chances of defeating the brontosaurus are one in seven, while the probability of defeating one of the stegosaurs is 1/2.

Which alternative should you choose? That is, which choice gives you the better chance of winning the game?

Hat Check Glitch

Last Problem:

A container holds 20 red balls and 30 blue balls. If you draw a ball out of the container without looking, what is the probability that it will be a red ball?

Answer:

The chances of drawing a red ball are 20/50 or 40%. The chances of drawing a blue ball are 30/50 or 60%.

Today’s Problem:

Six men check their hats at the theater. An inattentive attendant mixes up the claim checks, so when the men return after the show the hats are essentially handed out at random.

If someone offered you even money to bet that at least one of the men got his own hat back, would you take the bet? In other words, do you believe that the probability of one of the six men getting his own hat back to be greater than .5?

What is the Chance of Drawing a Red Ball?

Last Problem:

Three children make the following statements:

Child #1 [Frank]:

I am a truth teller.

Child #2:

Frank says he is a truth teller.

Child #3:

Frank is not a truth teller – he is a liar.

The three children quoted above are either truth tellers or liars. Can you tell with certainty how many of each there are?

Answer:

Child #1 [Frank] says he is a truth teller. The statement is true if he is telling the truth and false if he is lying.

What Child #2 says is true no matter whether the first child is telling the telling the truth or lying. Child #2 is therefore a truth teller.

The truth of Child #3 depends on the truthfulness of the first child (Frank). If the first child is lying, the third child is telling the truth. If the first child (Frank) is telling the truth, the third child is lying.

The possibilities are either [liar-truth teller – truth teller] or [truth teller – truth teller – liar]. Either way, two are telling the truth and one is lying. The question does not ask which child is telling the truth and which one is lying.

Today’s Problem:

A container holds 20 red balls and 30 blue balls. If you draw a ball out of the container without looking, what is the probability that it will be a red ball?

Truth Tellers or Liars?

Last Problem:

The will of an eccentric man stipulated that his two heirs were to stage a horse race and the owner of the losing horse would receive the entire inheritance. At the appointed hour, the race took place, but both heirs kept their horses from crossing the finish line. To break the stalemate, the executor of the will thought up a slight change to the race.

Following the executor’s idea, the two heirs raced again, and the one who finished first won the inheritance.

How could that be the case if everyone stayed true to the letter of the will?

Answer:

The two heirs swapped horses.

Today’s Problem:

Three children make the following statements:

Child #1 [Frank]:

I am a truth teller.

Child #2:

Frank says he is a truth teller.

Child #3:

Frank is not a truth teller – he is a liar.

The three children quoted above are either truth tellers or liars. Can you tell with certainty how many of each there are?

An Eccentric Will

Yesterday’s Problem:

A man ordered dinner at an expensive restaurant. When the meal was brought to him, he looked at it, wrote the above note for the waiter and left the restaurant. The waiter took the note to the cashier who understood its meaning and place it in the cash register. Can you figure out the meaning of the note?

Here is what the man wrote on the note he gave to the waiter:

102004180

Answer:

The note meant:

“I ought to owe nothing for I ate nothing.”

Today’s Problem:

The will of an eccentric man stipulated that his two heirs were to stage a horse race and the owner of the losing horse would receive the entire inheritance. At the appointed hour, the race took place, but both heirs kept their horses from crossing the finish line. To break the stalemate, the executor of the will thought up a slight change to the race.

Following the executor’s idea, the two heirs raced again, and the one who finished first won the inheritance.

How could that be the case if everyone stayed true to the letter of the will?

 

 

Decoding a Restaurant Note

Last Problem:

The word below may seem odd, but it is pronounced just like a common English word. Pronounce the “gh” as in “tough”, the “o” as in “women” and the “ti” as in “emotion.”

GHOTI

When then is the common word that GHOTI sounds like?

Answer:

Fish

Today’s Problem:

A man ordered dinner at an expensive restaurant. When the meal was brought to him, he looked at it, wrote the above note for the waiter and left the restaurant. The waiter took the note to the cashier who understood its meaning and place it in the cash register. Can you figure out the meaning of the note?

Here is what the man wrote on the note he gave to the waiter :

102004180