The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind

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] (#litres_trial_promo)

44. A shape sum

In the sum shown, different shapes represent different digits.

What digit does the square represent?

[SOLUTION] (#litres_trial_promo)

45. The pages of a newspaper

A newspaper has thirty-six pages.

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

[SOLUTION] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

Week 8 (#ulink_44197a9e-2266-5731-b2b7-7bb67f9fb6ca)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

52. Go on and on and on and on

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

What are the numbers in this sum?

[SOLUTION] (#litres_trial_promo)

53. A list of primes

Alice writes down a list of prime numbers less than 100, using each of the digits 1, 2, 3, 4 and 5 only once and using no other digits.

Which prime number must be in her list?

[SOLUTION] (#litres_trial_promo)

54. Continue the pattern

The diagram shows the first three patterns in a sequence in which each pattern has a square hole in the middle.

How many small shaded squares are needed to build the tenth pattern in the sequence?

[SOLUTION] (#litres_trial_promo)

55. How many codes?