Thinking Strategically - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Thinking Strategically.

Distinct Diagonals

Age 11 to 14 Short Challenge Level:

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

Multiplication Table Puzzle

Age 11 to 14 Short Challenge Level:

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?

Age 11 to 14 Short Challenge Level:

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?

Would You Like a Jelly Baby?

Age 11 to 14 Short Challenge Level:

What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?

Magic Error

Age 11 to 14 Short Challenge Level:

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

Subtracting to 2008

Age 11 to 14 Short Challenge Level:

Can you work out the sum of the missing digits in this subtraction?

Mini Kakuro

Age 11 to 14 Short Challenge Level:

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

Sevens

Age 11 to 14 Short Challenge Level:

What is the largest number Sophie can use to have seven positive integers with a mean of 7?

Magical Products

Age 11 to 14 Short Challenge Level:

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

Integral Polygons

Age 11 to 14 Short Challenge Level:

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?

Adjacent Additions

Age 14 to 16 Short Challenge Level:

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?

Facial Sums

Age 14 to 16 Short Challenge Level:

Can you make the numbers around each face of this solid add up to the same total?