Paul Godding's . . .

The Main Challenge

You roll two normal six-sided dice, both containing the numbers 1-6.  When multiplying the two numbers that show, how many DIFFERENT answers is it possible to obtain?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

What is the sum of the factors of 90?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are FOUR ways of making 49 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 49 by inserting 1, 2, 3 and 4 into the gaps on each line?

•  (◯+◯)²×(◯–◯)² = 49
•  (◯+◯)²×√◯–◯ = 49
•  ◯⁶–(◯+◯)×◯ = 49

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

What is the biggest integer (whole number) less than 630,000 that can be written using all six digits from 1 to 6?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

From the list, find three different numbers that have a sum of 100.

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are TWO ways of making 48 when using Lagrange’s Theorem. Can you find both?

Can you arrive at 48 by inserting 4, 4, 5 and 8 into the gaps on each line?

•  ◯×◯+◯+◯ = 48
•  ◯×◯×(◯–◯) = 48
•  ◯²+◯–(◯×◯) = 48

Answers can be found here.

Click Paul Godding for details of online maths tuition.

A warm Welsh welcome to 7puzzleblog.com and our compendium of daily number puzzles.

Five challenges are posted each day, seven days a week, and designed for our many followers from nearly 170 countries & territories throughout the world.

As well as our ever-expanding website of arithmetical challenges, this is also the place to learn about our successful venture into maths tuition.

The World’s #1 Daily Number Puzzle Website

When typing daily number puzzles into top search engines such as Google, Bing, Yahoo, Baidu, DuckDuckGo and Ecosia, you’ll see 7puzzleblog.com officially listed at #1 each time.

We appreciate and value your continued support.

Our aim

Simply to help improve basic knowledge and confidence of arithmetic in a fun way. Start your numerical adventure by trying to solve today’s five number puzzles.

How to use our website

As well as our latest challenges, simply access the remainder of our number puzzles by continually scrolling down the page.

Alternatively, to retrieve and attempt any particular day’s challenges from the past 12 months, just type in the address bar:

•  7puzzleblog.com/1 for DAY 1, through to . . .
•   7puzzleblog.com/366 for DAY 366

The Challenges

We have a vast collection of number puzzles, nearly 2,000 on this website, the majority of which are our very own creations.

They have been placed into seven categories:

The Main Challenge – involving different types of number puzzle gathered from all parts of the globe and will vary in content and difficulty from one day to the next.

The 7puzzle Challenge – linked to our signature puzzle board game, this is generally the easiest of the five daily number puzzles. Great for younger or less-confident students and will also improve their knowledge of mathematical terminology.

The Roll3Dice Challenge (DAYS 1 to 10) – puzzlers will be given seven groups of three numbers which replicate the rolling of three dice. The numbers in six of these groups can be manipulated to arrive at the target number, but your task is to find the impossible group of three numbers!

The Lagrange Challenge (DAYS 11 to 250) – named after the French-Italian mathematician who proved that every positive whole number can be made from adding together up to four square numbers. A medium-difficulty challenge where puzzlers must arrive at that particular day’s target number using his theorem.

The Factors Challenge (DAYS 251 to 366) – again related to that particular day’s number, puzzlers have to find which of the numbers listed, if any, are factors of the number in question (it will divide exactly into it). Good practice for ‘bus-stop’ division, and great to test some of the mathematical tricks available to find whether our number is a multiple of 2, 3, 4, 5 . . . and so on.

The Mathematically Possible Challenge – based on our best-selling arithmetic board game and designed to encourage creative number work. Challenges are also at the medium level of difficulty, but may require perseverance to find the possible answers!

The Target Challenge – hardest of the challenges, puzzlers must insert the given numbers into the correct gaps to arrive at the day’s target number. Can sometimes be tricky but will satisfy greatly when solved. A knowledge of BIDMAS, indices and estimation is desirable, but it will also help to think logically.

Copyright

We always encourage our number puzzles to be printed out for both fun and educational purposes in schools, home or work, but no part of this website may be republished or transmitted without prior permission and accreditation.

Puzzles & answers: Copyright © Paul Godding.

Spread the message

We’d really appreciate it if you could inform family, friends, students and colleagues about our fabulous daily number puzzles at 7puzzleblog.com. Please tell them there is no fee or registration required to access them, but most importantly that answers are provided!

You can get in touch by sending tweets to @7puzzle and e-mails to paul@7puzzle.com.

We hope you enjoy your visit.

Author, Paul Godding

The Main Challenge

If you multiply a certain number by 3 and then add 30, the result is the same as if you firstly added 17 to this particular number and then multiplied by 2.

Which number in the range 1 to 9 must this be?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

What is the product of the lowest number and highest number?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are TWO ways of making 47 when using Lagrange’s Theorem. Can you find both?

Can you arrive at 47 by inserting 2, 6, 7 and 10 into the gaps on each line?

•  ◯×◯+◯÷◯ = 47
•  ◯²–(◯+◯)÷◯ = 47
•  (◯+◯)²–(◯+◯) = 47

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

The smallest positive integer that has exactly three factors is FOUR; these are 1, 2 and 4. Find the next integer to have just three factors and the product of these three numbers.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 3rd & 7th rows contain the following fourteen numbers:

4   11   13   24   25   27   30   36   42   45   66   70   77   80

What is the sum of the multiples of 10?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are TWO ways of making 46 when using Lagrange’s Theorem. Can you find both?

Can you arrive at 46 by inserting 3, 4, 5 and 9 into the gaps on each line?

•  (◯+◯)×◯+◯ = 46
•  ◯²+◯×◯+◯ = 46
•  ◯×◯+◯–√◯ = 46

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

If you multiply two whole numbers together and then add 4, the result is 40. Which one of the following could NOT be the sum of the two whole numbers you initially multiplied?

12      13      15      18      20      37

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 2nd & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

Can you find four different numbers that have a sum of 100?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are FOUR ways of making 45 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 45 by inserting 2, 3, 5 and 6 into the gaps on each line?

•  (◯×◯÷◯)×◯ = 45
•  ◯²+◯×◯+◯ = 45
•  (◯+◯)×◯+◯ = 45

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

If the number sequence 2, 5, 8, 11, 14 . . . is continued, which is the ONLY number from the following list that will appear later in the sequence?

22   34   43   57   65   72   85   99

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 2nd & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

What is the difference between the sum of the odd numbers and the sum of the even numbers?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are TWO ways of making 44 when using Lagrange’s Theorem. Can you find both?

Can you arrive at 44 by inserting 2, 4, 6 and 7 into the gaps on each line?

•  (◯+◯)×(◯–◯) = 44
•  ◯²–(◯+◯)÷◯ = 44
•  (◯×◯–◯)×◯ = 44
•  ◯²+(◯–◯)×◯ = 44

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Using the numbers 2, 4 and 6 once each, together with + – × ÷, find the SIX target numbers from the following list that are mathematically possible to make:

12    14    16    18    20    22    24    26    28    30

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 2nd & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

What is the sum of the cube numbers?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are THREE ways of making 43 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 43 by inserting 4, 5, 8 and 9 into the gaps on each line?

•  ◯×◯–◯÷◯ = 43
•  ◯²+◯×(◯–◯) = 43
•  (◯+◯)×◯–◯² = 43
•  (◯×√◯×√◯)–◯ = 43
•  (◯–√◯)×◯+◯ = 43

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

You’ve rolled the numbers 2, 4 and 6 with your three dice.  Using these once each, with + – × ÷ available, find the THREE target numbers from 1-10 that it’s not possible to make.

Visit Roll3Dice.com for further details of similar challenges.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 2nd & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

Which three different numbers have a sum of 77?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are THREE ways of making 42 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 42 by inserting 2, 4, 6 and 8 into the gaps on each line?

•  ◯×(◯+◯)–◯ = 42
•  ◯²+(◯+◯)÷◯ = 42
•  ◯³–◯–(◯×◯) = 42

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

When a certain 4-digit number is multiplied by 4, its digits appear in reverse order. It also has both of these properties:

•  its first digit is a quarter of the last one, and
•  its second digit is one less than the first.

What number must it be?

The 7puzzle Challenge