The Five Legged Lamb

Abraham Lincoln once asked, "How many legs does a sheep have if you call its tail a leg?"

What do you think the correct answer is?

Four Goes Into Eighteen

A reader asks:

"How do you create a sum of eighteen using four numbers repeating none of them?"

This one should be pretty simple, can you figure it out?

A Fruity Problem

Professor Egghead's nephew spent a summer working as a stockboy for a large grocery store. It was a rather unusual grocery store, however, and they had a very strange way of arranging the fruit in the fresh produce area.

In one group you would find any of the following fruits:
apple, banana, grape, and orange.

In a different area you would find fruits like:
mango, nectarine, peach, and pear.

One day a new crate of fruit arrived and the young man wasn't sure where to put it. Where would you put a crate labeled strawberry?

What Color was the Bear?

A reader asks, "If a bear woke up, and began to walk, and every way he walked was south, what color was the bear and why?"

The 'Tree'mendous Apple Orchard

A certain farmer wanted to create a special orchard in the vacant field next to his house. He had been given ten special apple tree saplings: a Pink Lady, a CandyCrisp, a Fuji, a Cameo, a Granny Smith, a McIntosh, a Jonagold, a Red Delicious, a Senshu, and a Winesap. After careful consideration and planning it was decided that the apple trees would be planted so that there were five rows of trees with four trees in each row.

When he told his neighbors about his plan they all laughed and told him it was impossible to plant ten trees so that you have five rows of trees with four trees in each row.

The following year this is what his neighbors saw:

Click on the picture for a larger image


A few years later the same farmer was given six more apple trees: a Stayman, a Fortune, a Cortland, a Honeycrisp, a Macoun, and a Northern Spy. Six trees wasn't enough to create another star pattern of trees so he came up with a new plan. He changed the planned orchard and planted the six new trees so that all sixteen apple trees were placed in fifteen rows with four trees in each row.

What did the farmer's apple orchard look like when he was done?

Those Incredible Colored Socks

Professor Egghead woke up one morning and started dressing for a day in the office. He reached into his sock drawer and felt that there were four individual socks. He knew that two of those socks were black, one was white, and one was green. He grabbed two at random and put them on before leaving for work.

If one of the socks he was wearing was black, what is the probability that the other one was also black?

A Crossnumber Puzzle

Use the clues to fill in this crossnumber puzzle.

Clues
Across	Down
1. The cube of a whole number	1. A number that is unchanged if the digits are reversed
5. The number of square inches in a square yard	2. A prime number.
6. The number of cubic inches in a cubic foot.	3. The number of feet in a mile.
7. The number of millimeters in a meter.	4. The number of seconds in an hour.

Crossing the Bridge

Four men must cross an old bridge that spans a raging river. I'm not sure, but it might be the same river that the Victorian couples and the man with the tiger and goat needed to cross as well. The bridge is old and rickety and can only support two men crossing at once. To make matters even worse, it is pitch black and they have only one flashlight to share between them, which means that after two men have crossed one must return with the flashlight. Each of the men has differing abilities and some take more time to cross than the others. The times it takes for each man to cross are: 1 minute, 2 minutes, 5 minutes, and 10 minutes. When crossing in pairs, they can only cross as fast as the slowest man can go.

Can you find a way for all four men to cross in 17 minutes or less?

A Different Kind of Sudoku

Here's a sudoku challenge of a slightly different sort. In the 5x5 grid shown below, write (x,y) pairs, with x and y ranging from 1 to 5 inclusively, with the stipulation that x and y values cannot be repeated in any row, column, or diagonal.

For instance, if you write the (x,y) pair (1,3) in the top left cell, then you can not have any other pairs with an x value of 1 or a y value of 3 in the top row, the left-most column, or the main diagonal that runs from the top left to the bottom right.

This puzzle can be solved fairly quickly and is not quite as difficult as it may seem.


Click on the picture for a larger version

Behind the Green Door

You are a captive in a far away land. The king offers you your freedom if you can pass the following test:

You are placed in a room with two doors. Behind one door is a ferocious tiger, behind the other is your escape. 30 feet above each door is a window where a man is sitting. One man always tells the truth, the other is a constant liar. You may ask only one question.

What one question do you ask and to which man do you pose that question so that you are assured to reach freedom and not be eaten by the tiger. Remember; you don't know which man is honest and which one lies.

Simple Algebra

A reader of this page asks:

"If x²+y² = 36 and (x+y)² = 64, what is the value of x∙y?"

Help a fellow puzzle fan discover the values of x and y.

7 and 7 and 7 and 7 is 56

Using four 7s and any of the basic arithmetic operators (+, -, x, ÷) can you make 56?


7    7    7    7 = 56

Taking Notes

If six boys can fill up six notebooks in six weeks and four girls can fill up four notebooks in four weeks, how many notebooks can a class of twelve boys and twelve girls fill up in twelve weeks?

Change for a Dollar?

In the American money system, there are five coins in regular use. The penny is worth 1 cent, the nickel is worth 5 cents, the dime is worth 10 cents, the quarter is worth 25 cents, and the half-dollar is worth 50 cents.

If you use no more than 4 of any type of coin, how many different ways can you make change for 1 dollar (100 cents)?

More Barrels and More Pellets

In the puzzle Barrels Full of Pellets you were asked to find a way to discover which single barrel contained pellets that were slightly heavier than all the other barrels. This brain teaser is based on that one, but is considerably more difficult:


You are presented with ten barrels of pellets, but this time you are told that some or all *may* have 2 gram pellets and the rest have 1 gram pellets. You are given a scale for measuring and you are only allowed to take a measurement one time.

How do you find out which of the ten barrels have 1 gram pellets and which of the barrels have 2 gram pellets?

Hobos and Cigars

A certain hobo can make cigars from discarded cigar butts. He finds that with 5 cigar butts he can make one whole cigar.

One month he collects 25 butts. How many cigars can he make?

Artful Arithmetic

Professor Egghead had a student who was not very good with fractions and thought she had stumbled upon a quick way of discovering which of two fractions was the larger.

When she was asked to find the larger between 2/5 and 3/7 she simply subtracted the numerator from the denominator in each fraction, replacing them with 2/3 (2/(5-2)) and 3/4 (3/(7-3)) respectively, which she then replaced with 2/1 and 3/1, using the same method, and concluded that the first, 2/5, was the smaller.

Professor Egghead was impressed with her method. Was her method valid or was it complete nonsense and her correct answer only a lucky coincidence.

5 Times 2 = 7?

Using only basic arithmetic operations make 7 out of five '2's.


2    2    2    2    2 = 7


You can use '+', '-', 'x', or '÷' between the '2's.

Odd Arithmetic

Find four consecutive odd numbers that add up to 80.

Find five consecutive odd numbers that add up to 85.

The Motel Room

Three businessmen are in Cleveland for a convention. Since they are on a budget, they decide to share a room at a motel that charges $30 per night ($10 per man). The motel manager is in a good mood that night and decides to reimburse some of the money. He gives the bell boy $5 and tells him to give it to the three men. However, the bell boy is dishonest and figures that you cannot divide $5 evenly among three men, so he gives back $1 to each man and keeps the other $2 for himself.

Now, the businessmen have each paid $9 for the room, or $27 all together, and the bell boy has $2, for a total of $29.

What happened to the other $1?