Литагент HarperCollins - The Ultimate Mathematical Challenge - Over 365 puzzles to test your wits and excite your mind

The teacher in the classroom called ‘Square’ is next to the classrooms with the green and orange doors.

The classroom called ‘Cylinder’ is next to the classroom of the Science teacher.

English is taught in the classroom with the ‘unlucky’ prime number.

The classroom door of the Maths teacher is green.

The classroom numbers of Mrs Talbot and Mrs Richard add up to 30.

All the classroom door numbers are prime numbers.

The English teacher is next to a classroom that is next to the classroom of the Science teacher.

The teacher in the classroom with the red door likes rugby and is next to the Maths teacher.

The sum of all the classroom door numbers is 51.

The favourite sport of the teacher in the classroom named ‘Sphere’ is cricket.

The classroom called ‘Triangle’ is next door to the classrooms of the Art and Science teachers.

One of the classrooms has a white door.

[SOLUTION]

Week 23

155. Angles around a triangle

What is the value of a + b + c + d + e + f ?

[SOLUTION]

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?

[SOLUTION]

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?

[SOLUTION]

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?

[SOLUTION]

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]

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]

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]

Week 24

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]

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]

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]

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]

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]

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]

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]

Crossnumber 6

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)