This post contains the brain teasers and their answers.

**26Sept'07 Teaser:**

You have been promoted to pet detective while Ace Ventura guides some tourists on a safari. From the following clues, you must figure out who is the owner of each pet, and where the pet got lost.

1.A rabbit and a dog are two of the lost pets.

2.The pet lost in the garden is owned by Mary.

3.Robert does not own a dog.

4.John's pet was lost in the woods.

5.The cat was not lost in the woods or in the park.

**Answer:**

**I. Read the complete problem:**

Get a general idea of the problem. Here we have 3 owners, 3 pets, and 3 locations. You are being asked to match each pet with an owner and a location. A 3×3 table, also called a logic matrix, can be used to organize this information.

**II. Make a list of the members of each category:**

Owners: Mary, Robert, John

Pets: rabbit, dog, cat

Places: park, garden, woods

**III. Start filling the table with information from the clues**.

The clues may provide direct or deduced information and can be processed in any order. We start by putting the owner names in the top row. Here, we start with clue number 2:

*2. The pet lost in the garden is owned by Mary.*

Owners Mary John Robert

Pets

Places garden

*5. The cat was not lost in the woods or in the park.*

Therefore, the cat must have been lost in the garden.

Owners Mary John Robert

Pets cat

Places garden

*4. John's pet was lost in the woods....* and, therefore, Robert's pet must have been lost in the park.

Owners Mary John Robert

Pets cat

Places garden woods park

*1. A rabbit and a dog are two of the lost pets*.

*3. Robert does not own a dog.*

This means that Robert owns the rabbit, and John must own the dog.

**Owners Mary John Robert**

Pets cat dog rabbit

Places garden woods park

Congratulations! You now qualify as a pet detective.

**20Sep'07 Teaser:**

At an eBay auction, a woman's ring and a filigree jewelry box with a hand-painted ceramic top are on sale for $200.00 Dollars. The jewelry box is valued at $190.00 Dollars more than the ring. How much is the ring worth?

**Answer:**

If you said $10.00 Dollars, you are wrong! It is not that simple.

This is a problem that requires setting up two equations with two unknowns to find the answer.The box (B) plus the ring (R) cost $200.00 Dollars:

B + R = 200

The jewelry box is valued at $190.00 Dollars more than the ring, i.e., the price of the box (B) is equal to the price of the ring (R) plus $190.00 Dollars:

B = R + 190

Now we can substitute the right side of the second equation in the first equation and solve for R.

R + 190 + R = 200

2 R = 200 - 190

2 R = 10R = 10/2R = 5

*The ring is worth $5.00 Dollars. *

The price of the box is $190.00 plus $5.00, which is $195.00 Dollars, and the box plus the ring add up to $200.00. So, everything checks out.

**18Sep'07 Teaser:**

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

**Answer:**

This is a classic problem that many people get wrong because they reason that half of a hen cannot lay an egg, and a hen cannot lay half an egg. However, we can get a satisfactory solution by treating this as a purely mathematical problem where the numbers represent averages.

To solve the problem, we first need to find the rate at which the hens lay eggs. The problem can be represented by the following equation, where RATE is the number of eggs produced per hen per day:

1-1/2 hens × 1-1/2 days × RATE = 1-1/2 eggs

We convert this to fractions thus:

3/2 hens × 3/2 days × RATE = 3/2 eggs

Multiplying both sides of the equation by 2/3, we get:

1 hen × 3/2 days × RATE = 1 egg

Multiplying both sides of the equation again by 2/3 and solving for RATE, we get:

RATE = 2/3 eggs per hen per day.

Now that we know the rate at which hens lay eggs, we can calculate how many hens (H) can produce 12 eggs in six days using the following equation:

H hens × 6 days × 2/3 eggs per hen per day = 12 eggs

Solving for H, we get:

H = 12 /(6 × 2/3) = 12/4 = 3 hens.

Therefore, the farmer needs **3 hens to produce 12 eggs in 6 days.**

**17Sep'07 Teaser:**

A fruit vendor bought 100 pounds of berries for $2.00 per pound and expected to double his investment by selling the berries for $4.00 per pound at an open-air market. The vendor only managed to sell 50 pounds of berries the first day and he sold the remainder on the second day. The fresh berries had a content of 99% water, but because of the hot weather, the berries dehydrated and contained only 98% water on the second day. How much profit did the vendor make?

**Answer:**

The decrease of water content from 99% to 98% may seem insignificant, but it reduces the weight of the fruit by 50%. The 1% decrease in water content of the fruit should not be confused with a 1% decrease of the total amount of water, which would indeed be small.The cost of the berries is: 100 pounds × $2.00/pound = $200.00

The first day sale of berries with 99% water is: 50 pounds × $4.00/pound = $200.00. The vendor covers his cost on the first day, but does not make a profit.

On the second day, the berries have a water content of 98%. The weight of the dehydrated berries can be calculated as follows:

The leftover 50 pounds of berries with 99% water have 1% of non-water components which weigh 0.5 pound (50 pounds × 1/100 = 0.5 pounds).

When the berries dehydrate, the weight of the non-water component is still 0.5 pounds but it now comprises 2% of the total weight of the dehydrated fruit with the other 98% being water. The weight, W, of the dehydrated fruit can be calculated as follows:

0.5 pounds = W pounds 2% 100%W = (0.5×100)/2 = 25 pounds

What used to be 50 pounds of berries with 99% water content are now 25 pounds of berries with 98% water content.

The second day sale of berries with 98% water is: 25 pounds × $4.00/pound = $100.00. The profit is the total sales ($300.00) minus the cost ($200.00). **The vendor had a $100.00 Dollar profit.** The loss of water is also a loss of profits. This is why supermarkets spray water on fresh vegetables and keep produce refrigerated.

**13Sept'07 Teaser:**

A valuable painting was stolen from the Liar's Club, but the police are having a hard time identifying the culprit because every statement made by a member of the Liar's Club is false. Only four members visited the club on the day that the painting was stolen. This is what they told the police:

Ann: None of us took the painting. The painting was here when I left.

Bob: I arrived second. The painting was already gone.

Chuck: I was the third to arrive. The painting was here when I arrived.

Tom: Whoever stole the painting arrived before me. The painting was already gone.

Who of these four liars stole the painting?

**Answer:**

Since every statement is false, let us convert them into true statements, and number each statement:

Ann: 1) One of us took the painting. 2) The painting was gone when I left.

Bob: 3) I arrived first, third, or fourth. 4) The painting was still here.

Chuck: 5) I arrived first, second, or fourth. 6) The painting was gone when I arrived.

Tom: 7) Whoever stole the painting arrived after me. 8) The painting was still here.

According to statement #7, Tom is not the thief. #8: Since the painting was there when Tom arrived, he could not have been the last to arrive. Tom must have gone there first, second, or third. #6: The painting was gone when Chuck was there, so he didn't arrive first. #5: So Chuck got there second or fourth. #4 and #8: As two other members (Bob and Tom) arrived to see the painting, Chuck didn't get there second, either. So Chuck arrived fourth. #3: This means Bob arrived first or third. #2: Since the painting was gone when Ann left, she didn't arrive first. Otherwise, no member after her would have seen the painting. So Ann went there second or third and Chuck arrived fourth. But since two other members (Bob and Tom) saw the painting when they arrived, Ann didn't go there second, either. So Ann arrived third. #3: Therefore, Bob arrived first, and Tom arrived second.

In summary, Bob arrived first. Tom got there next and the painting was still there, so Bob was not the thief, and neither was Tom. When Ann arrived, the painting was still there, but it was gone when she left. So *Ann was the one who stole the painting*. Chuck arrived last and discovered that the painting was gone.

**12Sept'07 Teaser:**

At a bar, there is a bucket containing ice, some of which has melted. A bartender gets an ice cube weighing 20 grams from the ice bucket and puts it into an insulated cup containing 100 grams of water at 20 degrees Celsius. Will the ice cube melt completely? What will be the final temperature of the water in the cup?

**Answer:**

First of all, you have to know that the ice in the bucket has a temperature of 0 degrees Celsius. How do we know this? The Celsius temperature scale is defined to be 0°C when ice is in thermal equilibrium with water, and 100°C when water is in equilibrium with steam. An ice bucket does not provide extra cooling, it just maintains ice at its equilibrium melting point temperature.

The Specific Heat (Sh) of a substance is the amount of heat required to change the temperature of 1 gram of the substance by one degree Celsius. By definition, the Specific Heat of water is 1.0, and this amount of heat is called a calorie. A kilocalorie is 1000 calories, also called a "Calorie" with upper case. The Calories in nutrition labels are kilocalories.

Additional heat is required to change the state of a substance from solid to liquid, or from liquid to gas. This is called the "latent heat". Water is in thermal equilibrium with ice when it freezes at the same rate that the ice melts. The heat for melting or freezing water, also called the Heat of Fusion (Hf), is 80 calories per gram at 0°C, which is the equilibrium temperature. In other words, it is necessary to add 80 calories of energy to melt one gram of ice at 0°C. Conversely, it is necessary to remove 80 calories of energy to freeze one gram of water at 0°C. The heat for boiling or condensing water at 100°C, called the Heat of Vaporization, is 539 calories per gram, although this is not relevant to our problem. The following graph summarizes the effect of energy on the temperature of water in its solid, liquid, and gaseous phases.

The problem can be solved by breaking it into smaller pieces. The amount of energy needed to melt the ice is Wi×Hf, where Wi is the weight of the ice. In addition, the 20 grams of water obtained from the ice must be heated from 0°C, which is the temperature of the ice, to the final temperature Tf.

Where does the energy for melting the ice come from? Since the cup is insulated, the heat has to come from the 100 grams of water at 20°C. The amount of heat required to melt the ice and to increase the temperature of the resulting water to the final temperature is equal to the heat lost by the 100 grams of water. This can be expressed by an equation:

Wi×Hf + Wi×Sh×(Tf - 0°C) = Ww×Sh×(Twi - Tf)

WhereWi = weight of ice = 20g

Hf = Heat of fusion = 80 calories/gram

Ww = weight of water = 100gTf = final temperature,

Twi = initial water temperature = 20°C

Sh = Specific Heat for water = 1.0 calories per gram per °C

Substituting the values we get:

20×80 + 20×1×(Tf - 0°C) = 100×1×(20°C - Tf)1600 + 20Tf = 2000 - 100Tf120Tf = 400Tf = 400/120 = 3.3°C

*The final temperature is 3.3°C.* If we had had more ice or less water, there would not have been enough energy in the water to melt all the ice. Once the temperature of the water reaches 0°C, no more ice can melt.

*How much ice could be melted by 100 g of water at 20°C?* Using the equation above, where the final temperature is 0°C and the weight of the ice is unknown, we have:

Wi×80 = 100×1×20 The maximum amount of ice that could be melted is:

Wi = 2000/80 = 25 grams

*If the amount of ice exceeds 25 grams, the remainder will just float in 125 grams of water at 0°C.*

**11Sept'07 Teaser:**

A bear walks south for one kilometer, then it walks west for one kilometer, then it walks north for one kilometer and ends up at the same point from which it started. What color was the bear?

**Answer:**

The bear was white because it was a **polar bear**. The only place on earth where a bear can go south, west and north equal distances and end up where it started is the North Pole.

**10Sept'07 Teaser:**

There are twelve identical-looking balls, but one is either heavier or lighter than the other eleven. How can you determine which is the odd ball and find out whether this ball is heavier or lighter than the others using only three weighings with a balance?

**Answer:**

Label the balls from 1 to 12 to identify them.

Weigh 1, 2, 3, 4 against 5, 6, 7, 8:

I. If they balance, 9, 10, 11, 12 contain the odd ball.

Weigh 6, 7, 8 against 9, 10, 11.

a..If they balance, 12 is the odd ball. Weigh 12 against any other ball to discover whether it is heavy or light.

b..If 9, 10, 11 are heavy, they contain an odd heavy ball. Weigh 9 against 10. If they balance, 11 is the odd heavy ball, otherwise the heavier of 9 and 10 is the odd ball.

c.If 9, 10, 11 are light, we use the same procedure to reach the same conclusion for the odd light ball.

II.If 5, 6, 7, 8 are heavy, either they contain an odd heavy ball or 1, 2, 3, 4 contain an odd light ball.Weigh 1, 2, 5 against 3, 6, 10.

a.If they balance, the odd ball is 4 (light) or 7 or 8 (heavy). Weigh 7 against 8. If they balance 4 is light, otherwise the heavier of 7 and 8 is the odd heavy ball.

b.If 3, 6, 10 are heavy, the odd ball can be 6 (heavy) or 1 or 2 (light). Weigh 1 against 2. If they balance 6 is heavy, otherwise the lighter of 1 and 2 is the odd light ball.

c.If 3, 6, 10 are light, the odd ball is 3 and light or 5 and heavy. We thus weigh 3 against 10. If they balance, 5 is heavy, otherwise 3 is light.

III. If 5, 6, 7, 8 are light we use a similar procedure to that in II.

**7Sept'07 Teaser:**

An investor trading through a discount stock broker that charges $10.00 Dollars per transaction bought 200 shares of Vola Tile Corporation at $50.00 Dollars per share. The stock quickly increased in value by 50%, but then lost 40% of its value. The investor sold the stock. How much money did the investor gain or lose?

**Answer:**

The cost of 200 shares at $50.00 Dollars each is $10,000.00 Dollars.

The 50% gain on $10,000 is $5,000, making the new total $15,000.00 Dollars.

The 40% loss on $15,000 is $6,000, reducing the total amount to $9,000.00 Dollars.

This is a $1000.00 Dollar loss, plus $10 Dollars for the Buy transaction, and $10 Dollars for the Sell transaction.

The investor lost a total of $1020.00 Dollars.

It seems counterintuitive that the investor should lose money when the percentage of the loss is less than the percentage of the gain. However, the percentage of the loss is calculated on a bigger amount than the percentage of the gain.

**6Sept'07 Teaser:**

My sister has six red stamps and three blue ones. In her collection, seven stamps are from Mexico and six stamps are from France. One stamp is purple and it is not from Mexico or France. Two of her Mexican stamps are red and one is blue. Two of her French stamps are blue and three are red. How many stamps does she have?

**Answer:**

She has a minimum of 15 stamps.

Mexico: 1 blue, 2 red, 4 unknown color

France: 2 blue, 3 red, 1 unknown color

Unknown country: 1 purple, 1 red

... and for all we know, she might also have 2 green stamps from Germany.

**29Aug'07 Teaser:**

Three students checked into a hotel and paid the clerk $30 for a room ($10 each). When the hotel manager returned, he noticed that the clerk had incorrectly charged $30 instead of $25 for the room. The manager told the clerk to return $5 to the students. The clerk, knowing that the students would not be able to divide $5 evenly, decided to keep $2 and to give them only $3.

The students were very happy because they paid only $27 for the room ($9 each). However, if they paid $27 and the clerk kept $2, that adds up to $29. What happened to the other Dollar?

**Answer:**

The students have paid $27 and have kept $3 for themselves and that adds up to $30. Not a real puzzle... just a mistake in math! You cannot tally the clerks total twice, it's already included in the $27 the students have paid. The equation is incorrect...if they paid $27 and the clerk kept $2...then that does not add up to anything.

As far as the students are concerned, they paid $27 and received $3 change which adds up to $30, but the $27 Dollars obtained from subtracting $3 from $30 is just the result of a calculation and not an accounting of the real money. The confusion about the $2 Dollars kept by the clerk can be avoided by tracking down the real money.

**27Aug'07 Teaser:**

A scientist is experimenting with bacteria that are one micron in diameter and that reproduce by dividing every minute into two bacteria. At 12:00 PM, he puts a single organism in a container. At precisely 1:00 PM, the container is full.How big was the container?

**Answer:**

The number of bacteria in the container is 2n where n is the number of minutes elapsed. The full container has 260 (two to the sixtieth power), or approximately 1.153×1018 bacteria. Since one micron (one millionth of a meter) is 1×10-4 centimeters, each bacterium occupies a volume of about 1×10-12 cubic centimeters. Multiplying times the number of organisms, we conclude that the container had a capacity of 1.153×106 cc or 1,153 liters. The container was slightly bigger than one cubic meter.

260 = 1,152,921,504,606,846,976

**24Aug'07 Teaser:**

A scientist is experimenting with bacteria that are one micron in diameter and that reproduce by dividing every minute into two bacteria. At 12:00 PM, he puts a single organism in a container. At precisely 1:00 PM, the container is full.At what time was the container half full?

**Answer:**

The container was half full at 12:59 PM. When the bacteria doubled in the next minute, the container became full.

**23Aug'07 Teaser:**

A chicken farmer also has some cows for a total of 30 animals, and the animals have 74 legs in all. How many chickens does the farmer have?

**Answer:**

This is a typical algebra problem with two unknowns, and we need to have two equations to solve the problem. Let X be the number of cows, and Y the number of chickens.The number of cows plus the number of chickens equals 30:

X + Y = 30

Since cows have four legs and chickens have two legs, we can also have an equation for the number of legs.

4 X + 2 Y = 74

Rearranging the first equation we get

X = 30 - Y

Substituting X in the second equation gives us

4 × (30 - Y) + 2 Y = 74120 - 4 Y + 2 Y = 74-2 Y = 74 - 120 = -46Y = 23

**The farmer has 23 chickens. (and 7 cows).**

**22Aug'07 Teaser:**

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

**Answer:**

With two people (A and B), there is one handshake (A with B).

With three people (A, B, and C), there are three handshakes (A with B and C; B with C).

With four people (A, B, C, and D), there are six handshakes (A with B, C, and D; B with C and D; C with D).

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.

Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.

This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were **12 people at the party**.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

**21Aug'07 Teaser:**

You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?

**Answer:**

1.Fill the 3-liter bottle and pour it into the empty 5-liter bottle.

2.Fill the 3-liter bottle again, and pour enough to fill 5-liter bottle. This leaves exactly 1 liter in the 3-liter bottle.

3.Empty the 5-liter bottle; pour the remaining 1 liter from the 3-liter bottle into the 5-liter bottle.

4.Fill the 3-liter bottle and pour it into the 5-liter bottle. The 5-liter bottle now has exactly 4 liters.

*Here is another way to do it*

1.Fill the 5-liter bottle and pour water from it into the 3-liter bottle until it is full.This leaves 2 liters in the 5-liter bottle.

2.Empty the 3-liter bottle and pour the 2 liters of water from the 5-liter bottle into the 3-liter bottle.

3.Fill the 5-liter bottle again.

4.Fill the 3-liter bottle from the 5-liter bottle. Since the 3-liter bottle had 2 liters of water, only one liter is transferred leaving exactly 4 liters of water in the 5-liter jug.

**20Aug'07 Teaser:**

The grandson is about as many days old as the son is in weeks. The grandson is approximately as many months old as the father is in years. The ages of the grandson, the son, and the father add up to 120 years. What are their ages in years?

**Answer: **

Let G, S, and F represent the ages in years of the grandson, the son, and the father, respectively. Since a year has 365 days, or 52 weeks, or 12 months, the problem can be represented by three equations with three unknowns:

365 G = 52 S (The grandson is about as many days old as the son is in weeks)

12 G = F (The grandson is approximately as many months old as the father is in years)

G + S + F = 120 (The ages of the grandson, the son, and the father add up to 120 years)

Because the grandson's age is G = F/12, the son's age can be represented in terms of F by substituting:

S = (365/52)×GS = (365/52)×(F/12)

The third equation can now be represented with only the father's age as an unknown:

F/12 + (365/52)×(F/12) + F = 120

Multiplying by 12, we get:

F + (365/52)×F + 12 F = 120×12

20 F = 1440

F = 72

G = F/12 = 6

S = (365/52)×6 = 42

**The father is 72, the son is 42, and the grandson is 6 years old.**