This is part of our collection of Short Problems.

You may also be interested in our longer problems on Creating and Manipulating Linear and Quadratic Expressions Age 11-14 and Age 14-16

Printable worksheets containing selections of these problems are available here.

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### Starting Fibonacci

What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

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### No Matter

After performing some operations, what number is your answer always a multiple of?

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### Nine in a Line

The sum of 9 consecutive positive whole numbers is 2007. What is the largest of these numbers?

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### Paul's Children

Paul is 32 years old. In ten years time, Paul's age will be the sum of the ages of his three sons. What do his sons' ages add up to now?

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### Cube Pile

Rick has five cubes, each one 2cm taller than the previous one. The largest is the same height as a tower built of the two smallest. How high would a tower of all five cubes be?

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### 8 In a Row

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these integers?

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### Adding and multiplying

Amy misread a question and got an incorrect answer. What should the answer have be?

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### Sum and differences

Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?

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### Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

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### Multiple Magic

Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

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### Building Up

In the diagram, the number in each box is obtained by adding the two immediately below. What is the number in the top box?

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### Square Total

What is the smallest number Anastasia could have thought of, if after performing some operations, the total is a square number?

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### Standing on the Table

Clement and Dmitri both measure how much taller they are than the other when standing on a table. Can you work out how tall the table is?

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### Adding in Pairs

These are the results when 3 numbers were added in pairs. What were the numbers?

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### Forming Groups

Seventy pupils are divided into two groups. Can you work out the difference between the number of boys in group 1 and the number of girls in group 2?

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### Black and gold storeys

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

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### Square and Cube

The square of a positive number is twice as big as the cube of that number. What is the number?

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### Granny's Age

Weekly Problem 10 - 2015

Granny is four times as old as I am. Five years ago she was five times as old as I was. What is the sum of our ages?

Granny is four times as old as I am. Five years ago she was five times as old as I was. What is the sum of our ages?

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### Adding to 400

Find four integers whose sum is 400 and such that the first integer is equal to twice the second integer, three times the third integer and four times the fourth integer.

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### Brian's number

Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.

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### Big Fibonacci

The fifth term of a Fibonacci sequence is 2004. If all the terms are positive integers, what is the largest possible first term?

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### Months and Years

The product of Mary's age at her last birthday and her age in complete months is 1800. How old is Mary?