**UNDER CONSTRUCTION**

## Puzzle One: The Three Ages

An agriculturist tells a mathematician, "I have three plants. The product of their ages is seventy–two and they sum to my door number." The mathematician responds that it is not enough information. The agriculturist replies, "I need to go water my oldest plant." The mathematician smiles knowing their ages. How old are the plants?

## Puzzle Two: Crossing a Rickety Bridge at Night By Flashlight

Four people want to cross a bridge in the dark and only have one flashlight. The bridge is only strong enough to hold the weight of up to two people at a time and the people must cross with the help of flashlight. Different people can cross the bridge at different speeds but if together, must travel at the speed of the slowest person.

A needs 1 minute.

B needs 2 minutes.

C needs 5 minutes.

D needs 10 minutes.

What is the minimum amount of time required for everyone to cross the bridge?

A needs 1 minute.

B needs 2 minutes.

C needs 5 minutes.

D needs 10 minutes.

What is the minimum amount of time required for everyone to cross the bridge?

## Puzzle Three: Milk Tasting

Professional food tasters are coming to taste the milk your farm produces in an hour. You have 8 bottles of milk but one bottle has expired and you don't know which one. Looking around, you see your three pet hamsters. You can mix the milk from the different bottles into cups however you wish and feed one cup to each hamster. If any hamster drinks from a cup with any milk from the expired bottle, it will get sick in a little less than an hour. You have to feed the three hamsters once and at relatively the same time and then wait to see if any get sick. Doing this you can figure out which bottle is the expired one and not to serve to the food tasters. How do you do it? What mixture do you feed each hamster?

## Puzzle Four: Sixes the Hard Way

By adding any combination of simple math operations to each row, make each row equal to 6. For example, 2+2+2 = 6. You can add any number of operations to each row. You cannot use math functions like ceiling or floor or Fibonacci or trig functions. You cannot write anything with value like numbers, pi, phi, cube root (since you have to write a 3) but square root is fine. You do not need anything beyond what is learned in your first Algebra or Statistics class so no need for derivatives or integrals. You can use parenthesis however you like.

Hint: Do the easy ones first. If you get stuck, skip it and do a different one.

0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

10 10 10

Hint: Do the easy ones first. If you get stuck, skip it and do a different one.

0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

10 10 10

## Puzzle Five: Blue Eyes

100 perfect logicians with blue-eyes live on an island. No one knows the color of their own eyes but does know the color of the eyes of everyone else. (So each person knows all the others have blue eyes but he might have red eyes for example.) If anyone discovers that he has blue eyes, he must leave at 11 PM that day. Otherwise, everyone stays. If someone leaves, everyone will know of it. They cannot communicate to each other or determine the color of their own eyes in any way except with logic. They all know these rules.

One day, the voice of their (truthful) God rings down from the heavens and says: "Everyone on the island is hearing my voice. At least one person on the island has blue eyes."

Who leaves the island, and on what night? An interesting question is what information is gained by what the God says? What if instead of 100, it was n people?

One day, the voice of their (truthful) God rings down from the heavens and says: "Everyone on the island is hearing my voice. At least one person on the island has blue eyes."

Who leaves the island, and on what night? An interesting question is what information is gained by what the God says? What if instead of 100, it was n people?

## Puzzle Six: Glass Rearrangement

Six drinking glasses stand in a row, with the first three full of water and the next three empty. By handling and moving only one glass at a time, how can you arrange the six glasses so that they are still all in a row but no full glass stands next to another full glass, and no empty glass stands next to another empty glass. What is the minimum number of moves to solve this puzzle?

## Puzzle Seven: Lying About Their Age

Alex, Brook, Cody, Dusty, and Erin all share the same birthday but all are of different ages. Whenever one of them spoke to someone older, he or she was truthful. Whenever one of them spoke to someone younger, he or she lied. Today, on their birthday, I overheard them saying the following.* Dusty said to Brook: "I'm nine years older than Erin."...

* Erin said to Brook: "I'm seven years older than Alex."

* Alex said to Brook: "Your age is exactly 70% greater than mine."

* Brook said to Cody: "Erin is younger than you."

* Cody said to Dusty: "The difference between our ages is six years."

* Cody said to Alex: "I'm ten years older than you."

* Cody said to Alex: "Brook is younger than Dusty."

* Brook said to Cody: "The difference between your age and Dusty's is the same as the difference between Dusty's and Erin's."

How old is each person?

* Erin said to Brook: "I'm seven years older than Alex."

* Alex said to Brook: "Your age is exactly 70% greater than mine."

* Brook said to Cody: "Erin is younger than you."

* Cody said to Dusty: "The difference between our ages is six years."

* Cody said to Alex: "I'm ten years older than you."

* Cody said to Alex: "Brook is younger than Dusty."

* Brook said to Cody: "The difference between your age and Dusty's is the same as the difference between Dusty's and Erin's."

How old is each person?

## Puzzle Nine: Coin Flips

Three fair coins are flipped by a friend and all hidden from you. There are three deceptively similar cases of what happens. In each case, what is the probability that there are at least 2 heads?

Case 0 (Example)

No other information is given. In this case, the probability that there is at least 2 heads is 50%. You can work out the math or just realize that if there is not at least 2 heads, there are at least 2 tails, and these probabilities are equal and must add up to 100%. Thus, the chance there is at least 2 heads (or 2 tails) is 50%.

Case 1

He looks at the coins and tells you that at least one is heads.

Case 2

He looks at the coins and shows one to you, revealing a heads.

Case 3

You instead pick one at random to look at and see a heads.

Case 0 (Example)

No other information is given. In this case, the probability that there is at least 2 heads is 50%. You can work out the math or just realize that if there is not at least 2 heads, there are at least 2 tails, and these probabilities are equal and must add up to 100%. Thus, the chance there is at least 2 heads (or 2 tails) is 50%.

Case 1

He looks at the coins and tells you that at least one is heads.

Case 2

He looks at the coins and shows one to you, revealing a heads.

Case 3

You instead pick one at random to look at and see a heads.

## Puzzle Ten: How Tall?

How may you determine the height of a building using a barometer?

## Puzzle Eleven: Trivia?

1) What is the weight of a shadow?

2) What is the color of a mirror?

3) What is the southernmost, northernmost, easternmost, and westernmost state or territory of the United States?

4) What is the only state that can be typed using only one row of keys on a standard American Qwerty keyboard?

5) How do you parse the grammatically correct sentence: "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo."

6) Why would an English speaker organize digits this way?

8,5,4,9,1,7,6,3,2

7) To the same English speaker, what is the next number in this sequence?

3,3,5,4,4,3,5,5,4,3,?

2) What is the color of a mirror?

3) What is the southernmost, northernmost, easternmost, and westernmost state or territory of the United States?

4) What is the only state that can be typed using only one row of keys on a standard American Qwerty keyboard?

5) How do you parse the grammatically correct sentence: "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo."

6) Why would an English speaker organize digits this way?

8,5,4,9,1,7,6,3,2

7) To the same English speaker, what is the next number in this sequence?

3,3,5,4,4,3,5,5,4,3,?

## Puzzle Twelve: Birthday Girl

Albert and Bernard met Cheryl and asked her when her birthday is. Cheryl wrote down a list of ten possible dates.

May 15, May 16, May 19

June 17, June 18

July 14, July 16...

August 14, August 15, August 17

Cheryl whispered the month to one person and the day to the other. She tells them aloud that's what she did. “Can you figure it out now?” she asked.

Albert: “I don’t know when your birthday is, but I know Bernard doesn’t know, either.”

Bernard: “I didn’t know, but now I do.”

Albert: “Well, now I know, too!”

When is Cheryl’s birthday?

May 15, May 16, May 19

June 17, June 18

July 14, July 16...

August 14, August 15, August 17

Cheryl whispered the month to one person and the day to the other. She tells them aloud that's what she did. “Can you figure it out now?” she asked.

Albert: “I don’t know when your birthday is, but I know Bernard doesn’t know, either.”

Bernard: “I didn’t know, but now I do.”

Albert: “Well, now I know, too!”

When is Cheryl’s birthday?

## Puzzle Thirteen: Valentine's Apples

You know your Valentine loves apples so you bought her some. You have 3000 apples to give to your Valentine's 1000 miles away. Your truck can hold up to 1000 apples but you can't resist eating an apple for every mile you drive with them. You can, however, cache apples beside the road at any point. How many apples can you deliver? Only the maximum will win over the heart you desire.

## Puzzle Fourteen: Intertwined Fates

The apples worked! But your superstitious aunt has forbade the marriage unless you can prove your fates are intertwined. You will be shown an arbitrarily ordered Tarot deck of 52 different face up cards and must switch the locations of two cards. After you leave the room, that deck will be turned face down and shown to your loved one. Your loved one has to find a randomly-named card in that deck that you do not know beforehand and can turn over up to 26 cards in any order she chooses to do so. What strategy guarantees success?

## Puzzle Fifteen: Paint and Faint

Years of apple-filled happiness have passed since the wedding but a baby is coming soon and you still haven't finished the nursery? Your life partner has locked you there until each one of the four walls are painted the same color. Each wall is currently either pink or blue but the power outage means that you can't see their color nor tell the otherwise identical walls apart. Also, your endless supply of expired paint makes pink walls blue and blue walls pink and its smell causes you to faint regularly after painting up to two walls at a time. Each time you faint, you lose track of which walls are which and although you remember what you did, there is no way to tell which were painted last. How do you make sure each wall is the same color so you can get out of this mess?

## Puzzle Sixteen: Russian Roulette

A six-shooter revolver has four empty chambers and two adjacent bullets. After spinning the cylinder to a random chamber, I pull the trigger pointing at my head. I survive. Now your turn. Should you spin the cylinder randomly first or just pull the trigger? What are the odds for survival for each?

## Puzzle Seventeen: Square Pairs

Order the numbers 1-17 so that each adjacent pairs of numbers add up to a square number. For example 1,3,6,10 forms the sums 4, 9, and 16 but only contains four out of the seventeen numbers.

## Puzzle Eighteen: Self-Descriptive Number

What's a 10 digit number that describes itself so that the first digit is the number of 0's it contains, the second digit is the number of 1's, and so on? For example, a valid 4-digit solution is 1210.

## Puzzle Nineteen: Power Sequences

Consider the sequences: 0, 3, 5, 6 and 1, 2, 4, 7.

Note that their sum are equal and the sum of their squares are equal.

1. Make two sequences out of the numbers 0 through 15 that satisfy:

a. Their sums are equal.

b. The sum of their squares are equal.

c. The sum of their cubes are equal.

2. Make two sequences out of the numbers 0 through 31 that satisfy:

a. Their sums are equal.

b. The sum of their squares are equal.

c. The sum of their cubes are equal.

d. The sum of their fourth powers are equal.

3. Make a general rule such that for numbers 0 through 2^(k+1) - 1, your rule generates two sequences that satisfy these requirements up to the kth power.

4. Prove that it works for all higher values for k.

Note that their sum are equal and the sum of their squares are equal.

1. Make two sequences out of the numbers 0 through 15 that satisfy:

a. Their sums are equal.

b. The sum of their squares are equal.

c. The sum of their cubes are equal.

2. Make two sequences out of the numbers 0 through 31 that satisfy:

a. Their sums are equal.

b. The sum of their squares are equal.

c. The sum of their cubes are equal.

d. The sum of their fourth powers are equal.

3. Make a general rule such that for numbers 0 through 2^(k+1) - 1, your rule generates two sequences that satisfy these requirements up to the kth power.

4. Prove that it works for all higher values for k.

## Puzzle Twenty: Unlocked

You want to send a box of books to your friend but know that the contents will be stolen if the box is unlocked. You and your friend both have locks but neither has the other's key. How can you make sure the friend gets it?