Equations and Formulae - Short Problems

The number 2005 is the sum of a sequence of five consecutive positive integers. What is the smallest of these integers?

Luis writes down eight consecutive positive integers. The sum of the three smallest numbers is 33. What is the sum of the three largest numbers?

Given some relationships amongst these shapes, how many triangles equal one diamond?

This magic square has only been partially completed. Can you still solve it...

What number could replace x so that x/5 is between 3 and 4?

The Seven Dwarfs have seven different birthdays. How old can they be?

Using the new operator $\oplus$, can you solve this equation?

Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?

The numbers 2 to 8 are to be placed in the diagram so that the row and column each adds to 21. Which numbers can replace x?

Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one. What is the size of the smallest interior angle?

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

You may have seen magic squares before, but can you work out the missing numbers on this magic star?

Can you complete this magic square with the numbers from 7 to 15?

If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?

Can you find the solution to this equation? Each of the different letters stands for a different number.

Weighing the baby at the clinic was a problem. Can you work out the weight of the baby from the information given?

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?

For how many positive values of $n$ are both $\frac n2$ and $2n$ three-digit whole numbers?

Each row and column has the total given. What is the value of the heart symbol?

Can you find the sum of all of the numbers in the table?

Can you sum up the solutions to this equation?

Can you work out the product of $a$ and $b$ from the information in the question?

Can you work out how much this bat costs?

Can you work out Ali's age based on the diagram?

Can you find a pair of numbers such that their sum, product and quotient are all equal? Are there any other pairs?

Manipulate one algebraic fraction to solve another.

10 must remain within easy reach...

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

The planet Zog has both green and blue bank notes. Can you work out how many zogs two green and three blue bank notes are worth?

If $6x-y=21$ and $6y-x=14$, what is the value of $x-y$?

If you know how many books each boy, girl and teddy bear borrowed from the library, can you work out the number of girls?

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

Can you work out the angles of a triangle from the relationships between them?

Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

Can you solve this scary-looking equation?

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Will these vehicles fit through this tunnel?

Jasmine buys three different types of plant. How many triffids did she buy?

If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?

A table has blocks of wood placed on and next to it. Can you work out how tall it is?

Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it...

If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?

Al, Bertie, Chris and Di have sums of money totalling £150... What is the difference between the amount Al and Di have?

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

Can you work out how many spheres will balance a single pyramid?

Can you find the value of this expression, which contains infinitely nested square roots?

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?