Читать книгу The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind - Литагент HarperCollins USD, F. M. L. Thompson - Страница 20
Оглавление57. Three Tuesdays
Three Tuesdays of a month fall on even-numbered dates.
Which day of the week was the twenty-first day of the month?
58. Crack the code
In a seven-digit numerical code, each group of four adjacent digits adds to 16 and each group of five adjacent digits adds to 19.
What is the code?
59. Mr Bean’s fruit
Despite his name, Mr Bean likes to eat lots of fruit. He finds that four apples and two oranges cost £1.54 and that two oranges and four bananas cost £1.70.
How much would he have to pay if he bought one apple, one orange and one banana?
60. Ali’s bookshelves
Ali is arranging the books on his bookshelves. He puts half his books on the bottom shelf and two-thirds of what remains on the second shelf. Finally, he splits the rest of his books over the other two shelves so that the third shelf contains four more books than the top shelf. There are three books on the top shelf.
How many books are on the bottom shelf?
61. An unfair dice
I have an unfair dice that has probability of landing on a six, with all the other numbers equally likely. If the dice is thrown twice, what is the probability of obtaining a total score of ten?
62. A room in Ginkrail
The town of Ginkrail is inhabited entirely by knights and liars. Every sentence spoken by a knight is true, and every sentence spoken by a liar is false. One day some inhabitants of Ginkrail were alone in a room and three of them spoke.
The first one said: ‘There are no more than three of us in the room. All of us are liars.’
The second said: ‘There are no more than four of us in the room. Not all of us are liars.’
The third said: ‘There are five of us in the room. Three of us are liars.’
How many people were in the room and how many liars were among them?
63. Curious integers
In the following puzzle, each different capital letter represents a different digit. Thus ‘SEVEN’ represents a five-digit decimal number.
‘SEVEN’ is prime and, as one would expect, ‘SEVEN’ minus ‘THREE’ equals ‘FOUR’.
Curiously, ‘FOUR’ is prime (as is ‘RUOF’) but ‘THREE’ is not prime. Another oddity is that ‘TEN’ is a square.
Find the values of ‘FOUR’ and ‘TEN’.
