скачать книгу бесплатно
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
161. Maths, maths, Cayley
How many different solutions are there to this word sum, where each letter stands for a different non-zero digit?
[SOLUTION] (#litres_trial_promo)
Week 24 (#ulink_2ab90312-70ad-589c-966c-621f3c723d72)
162. An angle in a square
The diagram shows a square ABCD and an equilateral triangle ABE.
The point F lies on BC so that EC = EF.
Calculate the angle BEF.
[SOLUTION] (#litres_trial_promo)
163. Areas in a quarter circle
The diagram shows a quarter circle with centre O and two semicircular arcs with diameters OA and OB.
Calculate the ratio of the area of the region shaded grey to the area of the region shaded black.
[SOLUTION] (#litres_trial_promo)
164. How many extensions?
In a large office, each person has their own telephone extension consisting of three digits, but not all possible extensions are in use. To try to prevent wrong numbers, no used number can be converted to another just by swapping two of its digits.
What is the largest possible number of extensions in use in the office?
[SOLUTION] (#litres_trial_promo)
165. The top ball
Six pool balls numbered 1 to 6 are to be arranged in a triangle, as shown.
After three balls are placed in the bottom row, each of the remaining balls is placed so that its number is the difference of the two below it.
Which balls can land up at the top of the triangle?
[SOLUTION] (#litres_trial_promo)
166. Two squares
A square has four digits. When each digit is increased by 1, another square is formed.
What are the two squares?
[SOLUTION] (#litres_trial_promo)
167. Four vehicles
Four vehicles travelled along a road with constant speeds. The car overtook the scooter at 12:00 noon, then met the bike at 14:00 and the motorcycle at 16:00. The motorcycle met the scooter at 17:00 and overtook the bike at 18:00.
At what time did the bike and the scooter meet?
[SOLUTION] (#litres_trial_promo)
168. A marching band
A marching band is having difficulty lining up for a parade. When they line up in rows of 3, one person is left over. When they line up in rows of 4, two people are left over. When they line up in rows of 5, three people are left over. When they line up in rows of 6, four people are left over.
However, the band is able to line up in rows of 7 with nobody left over. What is the smallest possible number of marchers in the band?
[SOLUTION] (#litres_trial_promo)
Crossnumber 6 (#ulink_c1f643ff-f08c-5e86-908b-47a8cc0ae2ea)
ACROSS
1. A prime factor of 8765 (4)
4. The interior angle, in degrees, of a regular polygon; its digits have a product of 12 (3)
6. A Fibonacci number whose digits add up to twenty-four (3)
7. A prime that is one greater than a square (2)
8. Ninety-nine greater than the number formed by reversing the order of its digits (3)
10. A multiple of 25 ACROSS (3)
12. 9 DOWN multiplied by seven (3)
15. A number with seven factors (2)
17. The third side of a right-angled triangle with hypotenuse 9 DOWN and other side 25 ACROSS (2)
19. (10 ACROSS) per cent of 8 ACROSS (3)
21. An odd multiple of nine (3)
23. The product of the seventh prime and the eleventh prime (3)
25. An even number (2)
26. The lowest common multiple of 25 ACROSS and 11 DOWN (3)
28. A multiple of eleven, and also the mean of 12 ACROSS, 16 DOWN, 19 ACROSS, 24 DOWN and 27 DOWN (3)
29. A power of nineteen (4)
DOWN
2. An even square (3)
3. One third of 21 ACROSS (2)
4. The interior angle, in degrees, of the regular polygon that has twice as many sides as the regular polygon whose interior angle, in degrees, is 4 ACROSS (3)
5. One less than a multiple of eleven (3)
8. A power of nine (4)
9. The mean of 3 DOWN, 7 ACROSS, 13 DOWN, 17 ACROSS and 27 DOWN (2)
11. Ninety-one less than 10 ACROSS (2)
13. The sum of the squares of the digits of 23 ACROSS (2)
14. A factor of 4567 (4)
16. The difference between 11 DOWN and 3 DOWN (2)
18. The square root of 8 DOWN (2)
20. The highest common factor of 10 ACROSS and 24 DOWN (2)
21. The total number of days in a year in the months whose names do not contain the letter A (3)
22. A prime that is ten less than a cube (3)
24. A square multiplied by five; the product of its digits is 40 (3)
27. A triangular number that is the sum of two prime numbers that differ by eight (2)
[SOLUTION] (#litres_trial_promo)
Week 25 (#ulink_e0e86d87-357d-528d-ad4b-82ed7f1ff11a)
169. 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?
[SOLUTION] (#litres_trial_promo)
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.
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
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.
[SOLUTION] (#litres_trial_promo)
174. Bradley’s Bicycle Bazaar
