Which Door Do You Choose to Win the Parkinsons Recovery Cruise?

Last Problem:

How strongly do words affect perception? Practice reading the four lines of colored words below – but instead of saying the words, say the color of each word.

Can you say more than five words in a row without making a mistake? Or three?

Answer:

Well – of course there is no answer to this puzzle today. Why not give the challenge another trial run?

RED YELLOW BLUE GREEN

YELLOW BLUE GREEN RED

GREEN RED YELLOW BLUE

BLUE GREEN RED YELLOW

Today’s Problem:

Imagine if you will that you have been selected to be a guest on a game show that offers the chance to win a vacation on a Parkinsons Recovery Cruise. The prize sits behind one of the three doors: Monkeys (not real ones of  course) reside behind the other two doors.

You choose a door after much consternation. The host then opens one of the remaining two doors, revealing a monkey. The host then offers you a choice:

Stick with your initial choice or switch to the other door – still unopened of course.

What do you choose here? Stick with the door you initially chose or take the host up on the offer to peek inside the other door? The choice is important after all, since you will get to join others on a Parkinsons Recovery Cruise for free.

This puzzle should keep your neural networks firing for a few days!

Perception of Color and Words

Yesterday’s Problem:

When you throw a pair of dice, what are the chances that the number that comes up will be even?

Answer:

There are six possible even numbers that can come up : 2,4,6,8,10 and 12 – and only five possible odd numbers: 3,5,7,9 and 11. But, in spite of this, there are actually eighteen ways to throw an even number and eighteen ways to throw an odd number. So, this means the odds of an even number are indeed even.

You can easily see this by looking at the diagram below. The numbers of the two dice are listed in the top row and left most column. If you fill in the totals in the matrix, you will count 18 ways to throw an even number and 18 ways to throw an odd number. (Note that there are 36 total cells below).

1 2 3 4 5 6
1
2
3
4
5
6

Today’s Problem:

How strongly do words affect perception? Practice reading the four lines of colored words below – but instead of saying the words, say the color of each word.

Can you say more than five words in a row without making a mistake? Or three?

RED YELLOW BLUE GREEN

YELLOW BLUE GREEN RED

GREEN RED YELLOW BLUE

BLUE GREEN RED YELLOW

Rearrange the Letters

Last Problem:

How many different outcomes are possible in the toss of two coins? [Perhaps this is not so obvious as it might seem at first glance?]

Answer:

When most people think about this problem, the immediately answer that there are four possible outcomes: heads-heads, tails-tails, heads-tails and tails-heads.

But in reality, there can be a fifth possibility that mathematicians fails to acknowledge – uncountable. For example, one (or both) of the coins can land in the mud – or on a ledge – or drop down a sewer grate or be carried by an eagle in flight who caught the silvery coin it by its feet. The fifth probability of “uncountable” is not high, but it is also certain to occur occasionally.

Today’s Problem:

Can you rearrange the letters below to form one word in the space provided?

Rearrange the Two Words Below

N E W D O O R

To Make One Word

 

Two Coin Toss

Last Problem:

You begin a game with four cards. Two have a red pattern and two have a blue pattern and all are blank on one side.

You shuffle the four cards and place them face down. If you pick two cards at random, what is the probability that the two card will be the same color?

Your friend tries to convince you that the chances are 2/3 with this reasoning: There are three possibilities – two red, two blue or one of each – and since two of those are of the same color, the chances are two out of three. Are you convinced or not?

Answer:

The chances are not 2/3 but 1/3. The reasoning is simple. Choose any card. Of the three remaining cards, there can be only one that is the same color. The chances that you will pick it are only one in three.

Your friend has the problem figured incorrectly. The three possibilities he has identified are not equally as likely to happen.

Today’s Problem:

How many different outcomes are possible in the toss of two coins? [Perhaps this is not so obvious as it might seem at first glance?]

The Card Game: What is the Probability that …

Last Problem:

Which of the following statements is true”

1) One statement here is false.

2) Two statements here are false.

3) Three statements here are false.

Answer:

Only the second statement is true. Statement number 3 rules out both statement number 1 and statement number 3.

Today’s Problem:

You begin a game with four cards. Two have a red pattern and two have a blue pattern and all are blank on one side.

You shuffle the four cards and place them face down. If you pick two cards at random, what is the probability that the two card will be the same color?

Your friend tries to convince you that the chances are 2/3 with this reasoning: There are three possibilities – two red, two blue or one of each – and since two of those are of the same color, the chances are two out of three. Are you convinced or not?

Which of These Three Statements is True?

Yesterday’s Problem:

A teacher held up a piece of paper and asked his students to tell him how many squares they saw. His students replied:

Six, they replied.

Which was the correct answer.

The teacher then held up the paper again and asked his students how many squares they saw.

“Eight,” they replied, again correct.

How can this be? How many squares were really on the sheet? Six? Eight? Or?

Answer:

There were fourteen squares on the sheet – six on one side and eight on the other side.

Today’s Problem:

Which of the following statements is true:

1) One statement here is false.

2) Two statements here are false.

3) Three statements here are false.

How Many Squares Are There?

Last Problem

There is a secret word hidden in the following matrix of letters. Can you discover it? Can you unlock the code?

R V E O V C
S I O V R D
V E R C V O
R O V E S E
E R S C R I
C E R E O R

Answer:

If you count the letters, you will find there is 1 D, 2 I’s, 3 S’s, 4 C’s, 5 O’s, 6 V’s, 7 E’s and 8 R’s. The secret word is thus DISCOVER which is what you were ask to do in the problem. “Can you discover it?”

Today’s Problem:

A teacher held up a piece of paper and asked his students to tell him how many squares they saw. His students replied:

Six, they replied.

Which was the correct answer.

The teacher then held up the paper again and asked his students how many squares they saw.

“Eight,” they replied, again correct.

How can this be? How many squares were really on the sheet? Six? Eight? Or?