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

He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotating one domino.

What is the smallest number of moves he needs to make to arrange all the dominoes correctly?

[SOLUTION]

39. Mr Ross

Mr Ross always tells the truth on Thursdays and Fridays but always tells lies on Tuesdays. On the other days of the week he tells the truth or tells lies, at random. For seven consecutive days he was asked what his first name was, and on the first six days he gave the following answers, in order: John, Bob, John, Bob, Pit, Bob.

What was his answer on the seventh day?

[SOLUTION]

40. Missing number

Ria wants to write a number in each of the seven bounded regions in the diagram.

Two regions are neighbours if they share part of their boundary. The number in each region is to be the sum of the numbers in all of its neighbours.

Ria has already written in two of the numbers, as shown.

What number must she write in the central region?

[SOLUTION]

41. How many moves?

A puzzle starts with nine numbers placed in a grid, as shown.

On each move you are allowed to swap any two numbers. The aim is to arrange for the total of the numbers in each row to be a multiple of 3.

What is the smallest number of moves needed?

[SOLUTION]

42. The perimeter of a square

The diagram shows a square that has been divided into five congruent rectangles. The perimeter of each rectangle is 51 cm.

What is the perimeter of the square?

[SOLUTION]

Make a Number Challenge

In each case you are given some numbers and are challenged to use them to make the target number.

You can use the basic mathematical operations + − × ÷ and brackets, but no other mathematical symbols.

You can use each of the given numbers just once, but you don’t have to use all the numbers. You can’t put digits together to make larger numbers and you can’t use exponents.

Example : Use 1, 2, 3and 8to make 27.

Answer : (1 + 8) × 3 and 8 × 3 + 1 + 2 are both correct. However, 81 ÷ 3 and 3 1+2are not acceptable answers.

The following challenges are taken from the Primary Team Maths Resources for 2015.

Question 1

Use 1, 4, 4, 6, 6and 75to make 324.

Question 2

Use 1, 2, 4, 6, 7and 50to make 405.

Question 3

Use 1, 2, 3, 3, 6and 100to make 154.

Question 4

Use 1, 4, 5, 8, 9and 75to make 760.

Question 5

Use 5, 6, 8, 8, 9and 25to make 426.

Question 6

Use 1, 2, 4, 6, 7and 75to make 441.

Question 7

Use 1, 2, 3, 5, 7and 25to make 851.

Question 8

Use 2, 4, 5, 7, 8and 25to make 594.

Question 9

Use 1, 2, 6, 7, 8and 25to make 483.

Question 10

Use 1, 5, 6, 6, 7and 100to make 521.

[SOLUTION]

Week 7

43. Easter eggs

Mary has three brothers and four sisters.

If they, and Mary, all buy each other an Easter egg, how many eggs will be bought?

[SOLUTION]

44. A shape sum

In the sum shown, different shapes represent different digits.

What digit does the square represent?

[SOLUTION]

45. The pages of a newspaper

A newspaper has thirty-six pages.

Which other pages are on the same sheet as page 10?

[SOLUTION]

46. The sum of two primes

The number 12 345 can be expressed as the sum of two primes in exactly one way.

What is the larger of the two primes?

[SOLUTION]

47. A perimeter

The diagram shows three touching circles, each of radius 5 cm, and a line touching two of them.

What is the total length of the perimeter of the shaded region?

[SOLUTION]

48. The oldest tree

Today the combined age of three oak trees is exactly 900 years. When the youngest tree has reached the present age of the middle tree, the middle tree will be the present age of the oldest tree and four times the present age of the youngest tree.

What is the present age of the oldest tree?

[SOLUTION]

49. Who’s done their homework?

Miss Spelling, the English teacher, asked five of her students how many of the five of them had done their homework the day before. Daniel said none, Ellen said only one, Cara said exactly two, Zain said exactly three and Marcus said exactly four. Miss Spelling knew that the students who had not done their homework were not telling the truth but those who had done their homework were telling the truth.

How many of these students had done their homework the day before?

[SOLUTION]

Week 8

50. A stack of cubes

Katie writes a different positive integer on the top face of each of the fourteen cubes in the pyramid shown.

The sum of the nine integers written on the cubes in the bottom layer is 50. The integer written on each of the cubes in the middle and top layers of the pyramid is equal to the sum of the integers on the four cubes underneath it.

What is the greatest possible integer that she can write on the top cube?

[SOLUTION]

51. The largest remainder

Gregor divides 2015 successively by 1, 2, 3, and so on up to and including 1000. He writes down the remainder for each division.

What is the largest remainder he writes down?

[SOLUTION]

52. Go on and on and on and on

In this addition, G , N and O represent different digits, none of which is zero.