Paul Godding's . . .

The Main Challenge

If each letter is assigned a value as follows, A=1 B=2 C=3 . . . Z=26, can you find a 7-letter word in the English language that has the value of 79 when the values of all seven letters are added together?

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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

How many factors of 60 are listed above?

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 79 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 79 by inserting 2, 5, 9 and 10 into the gaps on each line?

•  (◯+◯)×◯+◯ = 79
•  (◯+◯)×◯–◯⁴ = 79
•  ◯²+◯×(◯–◯²) = 79

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

Using the three numbers 5, 5 and 5 once each, with + – × ÷ available, which SEVEN target numbers from 1-30 are mathematically possible to achieve?

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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which four different numbers 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 78 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 78 by inserting 2, 4, 5 and 8 into the gaps on each line?

•  ◯×◯×◯–√◯ = 78
•  (◯+◯)×(◯+◯) = 78
•  (◯²–◯)×◯+◯ = 78

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

The two sections below both contain eight letters, A to H.  Each letter has a calculation attached.  Which is the only letter to have the SAME answer in BOTH sections?

• Section 1

E:8×3   B:30÷2   H:15+3   A:6×6   G:36÷3   C:40–20   F:18+12   D:32–8

• Section 2

G:10+6   F:6×5   C:9×4   E:40÷2   H:30–18   A:15+9   D:30–12   B:120÷4

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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which two numbers have a difference of 36?

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 77 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 77 by inserting 2, 4, 5 and 7 into the gaps on each line?

•  ◯×(◯+◯+◯) = 77
•  ◯²+◯×(◯+◯) = 77
•  ◯×double(◯+◯)+◯ = 77

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

It is possible to use seven 4’s (4 4 4 4 4 4 and 4) once each, together with the four operations + – × ÷, to make all the different target numbers 1, 2, 3 and 4.

For instance, one way of arriving at the number 1 is:

4 – 4÷4 – 4÷4 – 4÷4 = 1

Can you show how to make the next three target numbers 2, 3 and 4?

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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

What is the sum of the multiples of 9?

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 FIVE ways of making 76 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 76 by inserting 6, 8, 10 and 12 into the gaps on each line?

•  ◯×◯+(◯–◯)² = 76  (2 different ways)
•  ◯×◯–(◯÷◯)² = 76
•  ◯×(◯–◯)+◯² = 76

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Start with the number 13, then follow these ten arithmetic steps:

–2   +5   ÷2   ×5   –4   ÷9   +1   ×5   –1   ÷4   =   ?

What is your final answer?

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which four different numbers, when added together, have a total 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 FIVE ways of making 75 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 75 by inserting 3, 4, 5 and 10 into the gaps on each line?

•  (◯+◯)×◯+◯ = 75
•  ◯²×(◯–◯–◯) = 75
•  ◯×◯+◯²+◯² = 75

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Can you arrive at the target answer of 24 by using the digits 2, 9, 13 and 13 exactly once each and with + – × ÷ available?

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which three numbers, when each is multiplied by 4, have their answers on the list?

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 FIVE ways of making 74 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 74 by inserting 4, 6, 7 and 8 into the gaps on each line?

•  ◯×◯+◯×◯ = 74
•  (◯+◯)×◯–◯² = 74
•  (◯+◯)×◯+◯ = 74

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

As well as 9+4+1, there are SEVEN other ways of making 14 when adding together three unique digits from 1-9.  List these seven combinations.

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

What is the sum of the multiples of 6?

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 FIVE ways of making 73 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 73 by inserting 2, 5, 7 and 8 into the gaps on each line?

•  ◯×◯×◯–◯ = 73
•  (◯+◯)×◯–◯ = 73
•  ◯²+◯×(◯–◯) = 73

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

From the numbers 1 to 20 inclusive, find the only one that remains when all square numbers, multiples of 6, factors of 40 and odd numbers are eliminated.

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

How many square numbers are present?

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 72 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 72 by inserting 4, 6, 8 and 10 into the gaps on each line?

•  ◯×◯+◯+◯ = 72
•  ◯×◯–(◯+√◯) = 72
•  (◯+◯)×◯+◯ = 72

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Allocate each letter of the English alphabet a numerical value, A=1 B=2 C=3 . . . Z=26. When adding the individual letters, find the total value of these four important words:

• KNOWLEDGE
• HARD WORK
• RESILIENCE
• ATTITUDE

If these were percentage values, there is a message for students here!

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which six numbers listed can each be made by adding three others from the list?

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 71 when using Lagrange’s Theorem. Can you find both?

Can you arrive at 71 by inserting 3, 5, 7 and 9 into the gaps on each line?

•  ◯×◯+◯+◯ = 71
•  ◯²+◯×◯–◯ = 71
•  (◯+◯)×◯–◯² = 71

Answers can be found here.

Click Paul Godding for details of online maths tuition.