35. Numbers around a circle
Five integers are written around a circle in such a way that no two or three consecutive numbers have a sum that is a multiple of 3. Of the five numbers, how many are themselves multiples of 3?
36. Digit sum 2001
Which is the smallest positive integer whose digits add up to 2001?
37. Seven semicircular arcs
The diagram shows a curve made from seven semicircular arcs, the radius of each of which is 1 cm, 2 cm, 4 cm or 8 cm.
What is the length of the curve?
38. Sorting dominoes
Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line, as shown in the diagram.
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?
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?
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?
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?
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?
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, 3 and 8 to make 27.
Answer: (1 + 8) × 3 and 8 × 3 + 1 + 2 are both correct. However, 81 ÷ 3 and 31+2 are not acceptable answers.
The following challenges are taken from the Primary Team Maths Resources for 2015.
Question 1
Use 1, 4, 4, 6, 6 and 75 to make 324.
Question 2
Use 1, 2, 4, 6, 7 and 50 to make 405.
Question 3
Use 1, 2, 3, 3, 6 and 100 to make 154.
Question 4
Use 1, 4, 5, 8, 9 and 75 to make 760.
Question 5
Use 5, 6, 8, 8, 9 and 25 to make 426.
Question 6
Use 1, 2, 4, 6, 7 and 75 to make 441.
