Mathematical Problems

A school bus travels from Veldhoven to Roosendaal. There are 4 children in the bus. And each child has 4 backpacks with him. There are 4 dogs sitting in each backpack. And every dog has 4 puppies with her. All these dogs have 4 legs, with 4 toes at each leg.

Using the digits 1 up to 9, two numbers must be made. The product of these two numbers should be as large as possible. All digits must be used exactly once.

Ronald and Michelle have two children. The probability that the first child is a girl, is 50%. The probability that the second child is a girl, is also 50%. Ronald and Michelle tell you that they have a daughter.

Charles walks over a railway-bridge. At the moment that he is just ten meters away from the middle of the bridge, he hears a train coming from behind. At that moment, the train, which travels at a speed of 90 km/h, is exactly as far away from the bridge as the bridge measures in length. Without hesitation, Charles rushes straight towards the train to get off the bridge. In this way, he misses the train by just four meters! If Charles would, however, have rushed exactly as fast in the other direction, the train would have hit him eight meters before the end of the bridge.

Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.

Patrick and Eric are on the two opposite banks of a river. They both have a rowing boat.

They both start off at the same time towards the opposite bank. They pass each other at 180 meters from the bank where Patrick departed. When reaching the opposite bank, they both take a rest for the same amount of time before they return. On the way back they pass each other at 100 meters from the bank from where Patrick returned.

Patrick and Eric both row with a constant speed, but Eric rows faster.

A rectangular room measures 7.5 meters in length and 3 meters in width. The room has a height of 3 meters. A spider sits 25 centimeters down from the ceiling at the middle of one of the short walls. A sleeping fly sits 25 centimeters up from the floor at the middle of the opposite wall. The spider wants to walk (i.e., move along the walls, floor, and ceiling only) to the fly to catch it.

On a nice summer day, two tourists visit the Dutch city of Gouda. During their tour through the center they spot a cosy terrace. They decide to have a drink and, as an appetizer, a portion of hot "bitterballs" (bitterballs are a Dutch delicacy, similar to croquettes). The waiter tells them that the bitterballs can be served in portions of 6, 9, or 20.

A salesman drives from Amsterdam to The Hague. The first half of the distance of his journey, he drives at a constant speed of 80 km/h. The second half of the distance of his journey, he drives at a constant speed of 120 km/h.

Consider a road with two cars, at a distance of 100 kilometers, driving towards each other. The left car drives at a speed of forty kilometers per hour and the right car at a speed of sixty kilometers per hour. A bird starts at the same location as the right car and flies at a speed of 80 kilometers per hour. When it reaches the left car it turns its direction, and when it reaches the right car it turns its direction again to the opposite, etcetera.

A swimmer jumps from a bridge over a canal and swims 1 kilometer stream up. After that first kilometer, he passes a floating cork. He continues swimming for half an hour and then turns around and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant effort.

The area of the square shown below is 8 x 8 = 64. The square is cut in the four parts A, B, C, and D, which are rearranged into the rectangle shown below. This rectangle has an area of 13 x 5 = 65.

Below we prove that 2=1:

Suppose that x = y. Then holds:

2x - x = 2y - y

This we can rewrite to:

2x - 2y = x - y

This we can rewrite to:

2 (x - y) = x - y

If we now divide by x - y, we get:

2 = 1

There is a water-cask with three different water-taps. With the smallest tap the water-cask can be filled in 20 minutes. With middle the tap the water-cask can be filled in 12 minutes. With the largest tap the water-cask can be filled in 5 minutes.

There is a unique number of ten digits, for which the following holds:

• all digits from 0 up to 9 occur exactly once in the number;
• the first digit is divisible by 1;
• the number formed by the first two digits is divisible by 2;
• the number formed by the first three digits is divisible by 3;
• the number formed by the first four digits is divisible by 4;
• the number formed by the first five digits is divisible by 5;
• the number formed by the first six digits is divisible by 6;
• the number formed by the first seven digits is divisible by 7;
• the number formed by the first eight digits is divisible by 8;
• the number formed by the first nine digits is divisible by 9;
• the number formed by the ten digits is divisible by 10.

In Mrs. Melanie's class are twenty-six children. None of the children was born on February 29th.

William lives in a street with house-numbers 8 up to 100. Lisa wants to know at which number William lives.

She asks him: "Is your number larger than 50?"
William answers, but lies.
Upon this, Lisa asks: "Is your number a multiple of 4?"
William answers, but lies again.
Then Lisa asks: "Is your number a square?"
William answers truthfully.
Upon this, Lisa says: "I know your number if you tell me whether the first digit is a 3."
William answers, but now we don't know whether he lies or speaks the truth.

Thereupon, Lisa says at which number she thinks William lives, but (of course) she is wrong.

Long ago, a young Chinese prince wanted to marry a Mandarin's daughter. The Mandarin decided to test the prince. He gave the prince two empty, porcelain vases, 100 white pearls, and 100 black pearls. "You must put all the pearls in the vases", he told the prince. "After this, I will call my daughter from the room next door. She will take a random pearl from one of the two vases. If this pearl is a black one, you are allowed to marry my daughter."

Below is an equation that isn't correct yet. By adding a number of plus signs and minus signs between the digits on the left side (without changes the order of the digits), the equation can be made correct.

123456789 = 100

From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808.

Postman Pat delivers the mail in the small village Tenhouses. This village, as you already suspected, has only one street with exactly ten houses, numbered from 1 up to and including 10.

In a certain week, Pat did not deliver any mail at two houses in the village; at the other houses he delivered mail three times each. Each working day he delivered mail at exactly four houses.

The sums of the house numbers where he delivered mail were:
on Monday: 18
on Tuesday: 12
on Wednesday: 23
on Thursday: 19
on Friday: 32
op Saturday: 25
on Sunday: he never works

On the market, mrs. Jones and mrs. Smith sell apples. Mrs. Jones sells her apples per two for 0.50 euro. The apples of Mrs. Smith are a bit smaller; she sells hers per three for 0.50 euro. At a certain moment, when both ladies have the same amount of apples left, Mrs. Smith is being called away. She asks her neighbour to take care of her goods. To make everything not too complicated, Mrs. Jones puts all apples to one big pile, and starts selling them for one euro per five apples. When Mrs. Smith returns at the end of the day, all apples have been sold. But when they start dividing the money, there appears to be a shortage of 3.50 euro.

A banana plantation is located next to a desert. The plantation owner has 3000 bananas that he wants to transport to the market by camel, across a 1000 kilometre stretch of desert. The owner has only one camel, which carries a maximum of 1000 bananas at any moment in time, and eats one banana every kilometre it travels.

Two friends, Alex and Bob, go to a bookshop, together with their sons Peter and Tim. All four of them buy some books; each book costs a whole amount in shillings. When they leave the bookshop, they notice that both fathers have spent 21 shillings more than their respective sons. Moreover, each of them paid per book the same amount of shillings as books that he bought. The difference between the number of books of Alex and Peter is five.

Consider 4 (dimensionless) flies, 2 males and 2 females. They are situated at the corners of 1 square meter. Every fly tries to reach the male/female fly in front of her/him. Their initial situation is visualized in the picture. Since the flies are flying towards another, they will meet each other at a certain time in the center of the square.

With all the numbers 0 up to 9 (using each number exactly once) you can make two fractions that add up to exactly 1.

A cyclist drove one kilometer, with the wind in his back, in three minutes and drove the same way back, against the wind in four minutes.

Greengrocer C. Carrot wants to expose his oranges neatly for sale. Doing this he discovers that one orange is left over when he places them in groups of three. The same happens if he tries to place them in groups of 5, 7, or 9 oranges. Only when he makes groups of 11 oranges, it fits exactly.

Calculate the minimum outside surface of a cylindrical bucket with an open upper side and which can hold 30 liters of water.

On a sunny morning, a greengrocer places 200 kilograms of cucumbers in cases in front of his shop. At that moment, the cucumbers are 99% water. In the afternoon, it turns out that it is the hottest day of the year, and as a result, the cucumbers dry out a little bit. At the end of the day, the greengrocer has not sold a single cucumber, and the cucumbers are only 98% water.

A number is called a palindrome when it is equal to the number you get when all its digits are reversed. For example, 2772 is a palindrome.

We discovered a curious thing. We took the number 461, reversed the digits, giving the number 164, and calculated the sum of these two numbers:

       461
       164 +
     -------
       625

We repeated the process of reversing the digits and calculating the sum two more times:

       625
       526 +
     -------
      1151
      1511 +
     -------
      2662

To our surprise, the result 2662 was a palindrome. We decided to see if this was a pure coincidence or not. So we took another 3-digit number, reversed it, which gave a larger number, and added the two. The result was not a palindrome.

We repeated the process, which resulted in another 3-digit number which was still not a palindrome. We had to repeat the process twice more to finally arrive at a 4-digit number which was a palindrome.

You walk upwards on an escalator, with a speed of 1 step per second. After 50 steps you are at the end. You turn around and run downwards with a speed of 5 steps per second. After 125 steps you are back at the beginning of the escalator.