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 44
Оглавление169. Non-factors of 720
Sam starts to list in ascending order every positive integer that is not a factor of 720.
Which is the tenth number in her list?
170. What size is JMO?
In the diagram, JK and ML are parallel. JK = KO = OJ = OM and LM = LO = LK.
Find the size of the angle JMO.
171. Amrita’s numbers
Amrita has written down four whole numbers. If she chooses three of her numbers at a time and adds up each triple, she obtains totals of 115, 153, 169 and 181.
What is the largest of Amrita’s numbers?
172. Where do the children come from?
Five children, boys Vince, Will and Zac, and girls Xenia and Yvonne, sit at a round table. They come from five different cities: Aberdeen, Belfast, Cardiff, Durham and Edinburgh. The child from Aberdeen sits between Zac and the child from Edinburgh. Neither of the two girls is sitting next to Will. Vince sits between Yvonne and the child from Durham. Zac writes to the child from Cardiff.
Where does each child come from?
173. Find four integers
Find four integers whose sum is 400 and such that the first integer is equal to twice the second integer, three times the third integer and four times the fourth integer.
174. Bradley’s Bicycle Bazaar
In the window of Bradley’s Bicycle Bazaar there are some unicycles, some bicycles and some tricycles. Laura sees that there are seven saddles in total, thirteen wheels in total and more bicycles than tricycles.
How many unicycles are in the window?
175. Liz and Mary’s problems
Liz and Mary compete in solving problems. Each of them is given the same list of 100 problems. For any problem, the first of them to solve it gets 4 points, while the second to solve it gets 1 point. Liz solved 60 problems, and Mary also solved 60 problems. Together, they got 312 points.
How many problems were solved by both of them?
