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 21
Оглавление64. Eight factors
A certain number has exactly eight factors including 1 and itself. Two of its factors are 21 and 35.
What is the number?
65. A nonagon problem
The diagram shows a regular nine-sided polygon (a nonagon or an enneagon) with two of the sides extended to meet at the point X.
What is the size of the acute angle at X?
66. How many primes?
Peter wrote a list of all the numbers that could be produced by changing one digit of the number 200.
How many of the numbers on Peter’s list are prime?
67. Fill in the blanks
Sam wants to complete the diagram so that each of the nine circles contains one of the digits from 1 to 9 inclusive and each contains a different digit.
Also, the digits in each of the three lines of four circles must have the same total. What is this total?
68. The school netball league
In our school netball league, a team gains a certain whole number of points if it wins a game, a lower whole number of points if it draws a game and no points if it loses a game.
After 10 games my team has won 7 games, drawn 3 and gained 44 points. My sister’s team has won 5 games, drawn 2 and lost 3.
How many points has her team gained?
69. How many zogs?
The currency used on the planet Zog consists of bank notes of a fixed size differing only in colour. Three green notes and eight blue notes are worth 46 zogs; eight green notes and three blue notes are worth 31 zogs.
How many zogs are two green notes and three blue notes worth?
70. How many V-numbers?
A three-digit integer is called a ‘V-number’ if the digits go ‘high-low-high’ – that is, if the tens digit is smaller than both the hundreds digit and the units (or ‘ones’) digit.
How many three-digit ‘V-numbers’ are there?
