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 41
Оглавление155. Angles around a triangle
What is the value of a + b + c + d + e + f?
156. Einstein sees two clocks
Albert Einstein was standing on the station platform thinking about relativity when he noticed he could see two station clocks. Each clock was digital, showing only hours and minutes. He observed that the display on one clock changed to the next minute 10 seconds before the correct time, whereas the display on the other clock changed to the next minute 10 seconds after the correct time.
For what fraction of the time did both clocks show the same time?
157. Halving an annulus
The shaded region in the diagram, bounded by two concentric circles, is called an annulus.
The circles have radii 2 cm and 14 cm. The dashed circle divides the area of this annulus into two equal areas.
What is its radius?
158. How many pairs?
How many pairs of numbers (a, b) exist such that the sum a + b, the product ab and the quotient of these two numbers are all equal?
159. Two ages
Abi and Becky were comparing their ages and found that Becky is as old as Abi was when Becky was as old as Abi had been when Becky was half as old as Abi is. The sum of their present ages is 44.
How old is Abi?
160. At McBride Academy
At McBride Academy there are 300 children, each of whom represents the school in both summer and winter sports. In summer, 60% of these play tennis and the other 40% play badminton. In winter, they play hockey or swim, but not both. 56% of the hockey players play tennis in the summer and 30% of the tennis players swim in the winter.
How many both swim and play badminton?
161. Maths, maths, Cayley
How many different solutions are there to this word sum, where each letter stands for a different non-zero digit?
