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?
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.
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.
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?
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?
166. Two squares
A square has four digits. When each digit is increased by 1, another square is formed.
What are the two squares?
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?
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?
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.
