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

How many zogs are two green notes and three blue notes worth?

[SOLUTION]

70. How many V-numbers?

A three-digit integer is called a ‘V-number’ if the digits go ‘high-low-high’ – that is, if the tens digit is smaller than both the hundreds digit and the units (or ‘ones’) digit.

How many three-digit ‘V-numbers’ are there?

[SOLUTION]

Shuttle Challenge 1

In the Shuttle rounds of the Team and Senior Team Maths Challenges, each team of four students is divided into two pairs who sit at opposite ends of a table. One pair tackles questions 1 and 3; the other pair attempts questions 2 and 4. The numerical answer to question 1 is passed across the table to the other pair who need it to answer question 2, and so on. The answer that is passed on is called A in the subsequent question.

The teams have eight minutes to answer all four questions. They get bonus marks if they answer all the questions correctly within six minutes.

How long will it take you?

Question 1

What is the value of (4 2+ 5 2) × 7 2?

Question 2

[ A is the answer to Question 1.]

At which number will the minute hand of a clock be pointing to ( A + 1) minutes after midnight?

Question 3

[ A is the answer to Question 2.]

John has three sticks that he has formed into a triangle. The length of each stick is a whole number of centimetres.

The length of one of the sticks is ( A + 1) cm, and the length of another of the sticks is ( A − 1) cm.

How many different possibilities are there for the length of John’s third stick?

Question 4

[ A is the answer to Question 3.]

A pyramid with a polygonal base has A faces.

How many edges does the pyramid have?

[SOLUTION]

Week 11

71. A magic square

In a magic square, each row, each column and both main diagonals have the same total.

In the partially completed magic square shown, what number should replace N ?

[SOLUTION]

72. Fly, fly, fly away

In this addition sum, each letter represents a different non-zero digit.

What are the numbers in this sum?

[SOLUTION]

73. What is the units digit?

Catherine’s computer correctly calculates

What is the units digit of its answer?

[SOLUTION]

74. Minnie’s training

After a year’s training, Minnie Midriffe increases her average speed in the London Marathon by 25%.

By what percentage did her time decrease?

[SOLUTION]

75. Telling the truth

The Queen of Hearts always lies for the whole day or always tells the truth for the whole day.

Which of these statements can she never say?

A. ‘Yesterday, I told the truth.’

B. ‘Yesterday, I lied.’

C. ‘Today, I tell the truth.’

D. ‘Today, I lie.’

E. ‘Tomorrow, I shall tell the truth.’

[SOLUTION]

76. What is the unshaded area?

Eight congruent semicircles are drawn inside a square of side length 4.

Each semicircle begins at a vertex of the square and ends at a midpoint of an edge of the square.

What is the area of the unshaded part of the square?

[SOLUTION]

77. Aimee goes to work

Every day, Aimee goes up an escalator on her journey to work. If she stands still, it takes her 60 seconds to travel from the bottom to the top. One day the escalator was broken so she had to walk up it. This took her 90 seconds.

How many seconds would it take her to travel up the escalator if she walked up at the same speed as before while it was working?

[SOLUTION]

Week 12

78. The pages of a book

The pages of a book are numbered 1, 2, 3, and so on. In total, it takes 852 digits to number all the pages of the book. What is the number of the last page?

[SOLUTION]

79. A letter sum

Each letter in the sum shown represents a different digit.

The letter A represents an odd digit.

What are the numbers in this sum?

[SOLUTION]

80. Timi’s ears

Three inhabitants of the planet Zog met in a crater and counted each other’s ears. Imi said, ‘I can see exactly 8 ears’; Dimi said, ‘I can see exactly 7 ears’; Timi said, ‘I can see exactly 5 ears.’ None of them could see their own ears.

How many ears does Timi have?

[SOLUTION]

81. Unusual noughts and crosses

In this unusual game of noughts and crosses, the first player to form a line of three Os or three Xs loses.

It is X’s turn. Where should she place her cross to make sure that she does not lose?

[SOLUTION]

82. An average

The average of 16 different positive integers is 16.

What is the greatest possible value that any of these integers could have?

[SOLUTION]

83. Painting a cube

Each face of a cube is painted with a different colour from a selection of six colours.

How many different-looking cubes can be made in this way?

[SOLUTION]

84. A Suko puzzle

In the puzzle Suko, the numbers from 1 to 9 are to be placed in the spaces (one number in each) so that the number in each circle is equal to the sum of the numbers in the four surrounding spaces.

How many solutions are there to the Suko puzzle shown?

[SOLUTION]

Crossnumber 3

ACROSS

2. The sum of a square and a cube (3)

4. Nine less than half 26 ACROSS (2)

6. 13 DOWN plus 5 DOWN minus 2 ACROSS minus 10 DOWN (3)

7. A prime factor of (6 ACROSS plus 15) (2)

8. The square root of 4 ACROSS cubed (2)

9. One more than a multiple of 8 (3)

12. Fifteen less than a cube (2)

14. A multiple of fourteen (3)

17. A prime greater than 13 and whose digits are different (2)

18. The mean of 5 DOWN, 21 DOWN and 28 ACROSS (2)

19. Three more than a square (3)

22. An even number that is less than 24 DOWN (2)

24. The sum of 9 ACROSS and a multiple of five (3)

26. The difference of two two-digit triangular numbers and also one more than an odd square (2)

28. The first two digits of the square of 17 ACROSS (2)

29. The hypotenuse of a triangle whose shorter sides are 21 DOWN and 20 DOWN (3)

30. The lowest common multiple of 10 DOWN and 15 DOWN (2)

31. A factor of 6789 (3)

DOWN

1. The square of (one more than a multiple of 29) (4)

2. A prime factor of 2008 (3)

3. A Fibonacci number that is one more than 2 ACROSS (3)

5. Two less than 11 DOWN minus 4 ACROSS (2)

10. Eight more than half 4 ACROSS (2)

11. The sum of a Fibonacci number and a triangular number in three distinct ways (2)

13. The number whose digits are those of 31 ACROSS reversed (3)

14. 3 DOWN plus 11 DOWN (3)

15. A multiple of 5 that is less than 16 DOWN (2)

16. A power of 2 that is greater than 4 ACROSS and less than 28 ACROSS (2)

20. The exterior angle, in degrees, of a regular polygon (2)

21. 70 per cent of 30 ACROSS (2)

23. A prime whose digits are increasing consecutive numbers (4)