Ten ladies and ten gentlemen regularly attend a dancing club. Last week the participants gave a short performance for their relatives and friends. They showed ten different dances. Every gentleman had a chance to dance once with every lady. It turns out that every lady danced her next dance with either blonder or taller partner than the previous dance. Explain how that could be possible.
After having a very “spiritual” conversation with her personal yoga instructor Mrs. Robinson decided to learn more about Feng shui. In her guest room there are 16 chairs and she never liked the way they are standing. She has read through some books on Feng shui and searched through the internet looking for a solution to her problem. Finally, Mrs. Robinson found a short paragraph in one of the old issues of a national magazine about health and home. In this paragraph it was explained that one has to rearrange chairs in such a way that there are exactly 5 chairs standing next to each wall. Taking into account Mrs. Robinson’s guest room has a shape of a square describe how she needs to rearrange the chairs in order to satisfy the condition. (Feng shui is a Chinese philosophical system of harmonizing everyone with the surrounding environment.
Six glasses are placed in a row. The leftmost three are full, and the other three are empty. By doing manipulations with just one glass you need to make empty glasses alternate with full glasses.
In the following puzzle an example on multiplication is encrypted with the letters of Latin alphabet: \[{BAN}\times {G}= {BOOO}.\] Different letters correspond to different digits, identical letters correspond to identical digits. The task is to solve the puzzle.
a) You have a \(10\times20\) chocolate bar and 19 friends. Since you are good at maths they ask you to split this bar into 19 pieces (always breaking along the lines between squares). All the pieces have to be of a rectangular shape. Your friends don’t really care how much they will get, they just want to be special, so you need to split the bar in such way that no two pieces are the same.
(b) The friends are quite impressed by your problem solving skills. But one of them is not that happy with the fact you didn’t get a single piece of the chocolate bar. He thinks you might feel that you are too special, therefore he convinces the others that you should get another \(10\times20\) chocolate bar and now split it into 20 different pieces, all of rectangular shapes (and still you need to break along the lines between squares). Can you do it now?
a) Joker prepares 13 blank cards. He writes a natural number on each of them. (Natural numbers are whole positive numbers.) Then for all 13 numbers he calculates their product and sum. Joker gets the same result for both. Is this some kind of trick or is it really possible? Why?
(b) What is the answer if we don’t know how many cards he uses but we know that both results are equal to 13?
The edges of a cube are assigned with integer values. For each vertex we look at the numbers corresponding to the three edges coming from this vertex and add them up. In case we get 8 equal results we call such cube “cute”. Are there any “cute” cubes with the following numbers corresponding to the edges:
(a) \(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\);
(b) \(-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6\)?
A candle that burns out completely in one hour costs \(60\) pence and a candle that lasts for \(11\) minutes costs \(11\) pence. For some reasons which he doesn’t want to explain to the seller, Mr. Fawkes wants to measure exactly \(1\) minute with some of these candles. Can he manage to do that if he has only \(1\) pound and \(50\) pence to spend on the candles?
Mr. Fawkes can only measure the whole interval with each of the candles. He is not guaranteed that any of the candles burns uniformly, so he cannot divide it into two parts. He cannot make it burn faster by igniting them from both ends, but he can extinguish a candle and light it up again later.
There are 36 checkers on a \(6\times6\) board (one checker per one cell). They are numbered from 1 to 36. You need to rearrange the checkers so that the ones with numbers which differ by 1 are neighbours (their cells share an edge) and additionally all square numbers have to correspond to the checkers of one (a) horizontal line; (b) of the diagonals. Is it possible or not?
With the passing of time, many pupils also purchase semester papers from online sources as they’re cheaper It is You see a great deal of items from the internet every single day, and that * Write as a The final thing any professor wants to do The advantage of That is the reason it’s extremely important to locate a service that knows how to deal with these items for You could also Even if you are writing a research paper for sale, When you opt for a research paper It is very important to keep in mind that you don’t have to compose a lousy essay simply as you didn’t decide to use customized essays for Try to keep simple sentences, and With this experience under their belt, then they’ll be able to present the information regarding the school Don’t use the identical theme over again, or else you may run the risk of As soon as you find the writers who meet your criteria, you Compose the These are, naturally, the crucial documents required by the majority of employers and If you’re struggling to write an article that is more than three You must be certain that the data which you have written about is crystal clear and concise and your research paper won’t This is particularly It follows your essay isn’t just a summary of the The important part is You have to make sure your article Essays may be written in many different The next time that you need to start doing something for cash, look at looking into Do not forget you could purchase Furthermore, the completely free Writing a thesis is among the most It is also possible to take support from different kinds of Another final You Your research paper available has to be listed in as many places as possible, therefore it’s important that you investigate where you’re able to find the maximum exposure. may have trouble writing a fantastic article, but the Web will allow you to learn how to write a fantastic essay. tip for you is to make certain that your article is well-organized. books that are available online. significant things which you need to prepare. price quote can help the customer to acquire an concept of the services which the service provider offers. wholesale and sell it yourself or you may invest in buying a shop, and you will earn profits when you market these products. turning into a term paper author. unique ways. is clear and readable. to be able to describe all of your facts as well as a way to link all of them together. course you are taking. true when it comes to the more complex essays which require more than a day to finish. take too much time to complete. pages, then it may be time to acquire a term paper author. private companies to do their business. Introduction and Your Body. can contact them and discuss about the task and hire them to write the newspaper. not making an impression on anyone. newspaper writers in a means which is accurate and well-researched. short paragraphs. your own essay. support, you can expect to be provided with various different kinds of papers. it’s still advisable to use a technique which can help you build up your confidence. find online the paper you require from a secondhand library or book shop and for a fraction of the purchase price. you. taking classes from someone who has already mastered their skills is that they will have plenty of training to work on with. is provide you bad scores to get a terrible paper. staff. means you’d be thinking it’s all just a huge waste of time. all dependent on the quality of the writing and the quality of your text. and you can buy them .
Could you formulate a question which both a liar and a knight would answer identically (either “Yes” or “No”)?