Thinking Strategically - Lower Secondary

Thinking Strategically is part of our Thinking Mathematically collection.

Dozens

Stage: 3 Challenge Level: Challenge Level:1

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Got It

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

The Queen of Hearts

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 33 - 2011
The Queen of Hearts has lost her tarts! She asks each knave if he has eaten them, but how many of them are honest...

Unequal Exam

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Weekly Problem 18 - 2013
120 students sit an exam with 100 marks available. What is the smallest number of pairs that are awarded the same mark?

Square It

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Integral Polygons

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 51 - 2012
Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?

Total Totality

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 25 - 2013
Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?

Four in a Row

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Weekly Problem 31 - 2013
Where should black play in this game of four-in-a-row to be certain of winning on her next move?

Warmsnug Double Glazing

Stage: 3 Challenge Level: Challenge Level:1

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Factors and Multiples Game

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A game in which players take it in turns to choose a number. Can you block your opponent?

Diamond Collector

Stage: 3 Challenge Level: Challenge Level:1

Collect as many diamonds as you can by drawing three straight lines.

Mini Kakuro

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 21 - 2008
The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

Connect Three

Stage: 3 Challenge Level: Challenge Level:1

Can you be the first to complete a row of three?

Crossing the Bridge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Cops and Robbers

Stage: 2 and 3 Challenge Level: Challenge Level:1

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Dicey Operations

Stage: 2 and 3 Challenge Level: Challenge Level:1

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Alphabetical Discovery

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Weekly Problem 11 - 2010
Can you DISCOVER the smallest solution to this word problem...

Distinct Diagonals

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 21 - 2010
How many diagonals can you draw on this square...

Facial Sums

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 41 - 2010
Can you make the numbers around each face of this solid add up to the same total?

Draught Plans

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 9 - 2011
Barbara is putting draughts on a $4x4$ board in a particular way. Can you find the least number of draughts she needs to put down?

Magical Products

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Weekly Problem 9 - 2013
Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

Would You Like a Jelly Baby?

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 9 - 2014
What is the smallest number of jelly babies Matt needs to remove from his pocket to guarentee he gets at least one of each flavour?

Magic Error

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 12 - 2014
Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?

Whitewater Rafting

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 20 - 2014
How many journeys does it take for two adults and two children to cross a river using only an unstable raft?

Subtracting to 2008

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 2 - 2015
Can you work out the sum of the missing digits in this subtraction?

Adjacent Additions

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 3 - 2015
In a 7-digit numerical code, each group of four consecutive digits adds to 16, and each group of five consecutive digits adds to 19. What is the sum of all 7 digits?

Spot the Fake

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 47 - 2015
One of N coins is slightly heavier than the others. How large can N be if the coin can be determined with only two weighings with a set of scales?

11x11 Square

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Here's a neat trick you can do with an 11 by 11 square...

River Crossing

Stage: 3 Challenge Level: Challenge Level:1

There is nothing half so much worth doing as simply messing about in boats...

Sevens

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 4 - 2016
What is the largest number Sophie can use to have 7 positive integers with a mean of 7?

Multiplication Table Puzzle

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 6 - 2017
In the multiplication table on the right, only some of the numbers have been given. What is the value of A+B+C+D+E?

What's on the Back?

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 21 - 2017
Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?

Thinking Strategically - Short Problems

Stage: 3 and 4

A collection of short Stage 3 and 4 problems on Thinking Strategically.