Paul Godding's . . .

The Main Challenge

Here is a unique 7-part question. Answer all seven parts:

1.  (4 + 3) + (2 – 1)  =  ?
2.  (4 × 3) ÷ (1 × 1)  =  ?
3.  (4 – 3) × (2 ÷ 1)  =  ?
4.  (3 + 3) ÷ (2 × 1)  =  ?
5.  (3 ÷ 3) – (1 + 1)  =  ?
6.  (3 – 3) × (1 ÷ 1)  =  ?
7.  (3 × 3) – (2 + 1)  =  ?

Now find the sum of all seven answers.

What is your overall answer?

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the difference between the two multiples of 8?

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 just THREE ways of making 113 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 113 by inserting 7, 10, 12 and 14 into the gaps on both lines?

•  ◯×◯+◯–◯ = 113
•  ◯²–(◯+◯+◯) = 113

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

If you multiply a mystery number by 6 and then subtract 6, the result is the same as if you first multiplied the same mystery number by 3 and then added 3.

Is the value of this mystery number 1, 2, 3, 4 or 5?

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the sum of the multiples of 7 listed?

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 just THREE ways of making 112 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 112 by inserting 3, 5, 10 and 11 into the gaps on both lines?

•  ◯×◯+◯–◯ = 112
•  (◯+◯)×(◯–◯) = 112

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

This describes a particular number less than 100:

•  its digits add up to 12,
•  if the unit digit is subtracted from the tens digit, then doubled, the answer is also 12.

What is the number?

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

List THREE different numbers that 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 FIVE ways of making 111 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 111 by inserting 2, 3, 5 and 7 into the gaps on both lines?

•  (◯×◯+◯)×◯ = 111
•  (◯+◯)²+double(◯×◯) = 111

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Carry out these instructions in our 7-step challenge:

1.  Work out the sum of 4 and 6,
2.  Calculate the product of 4 and 6,
3.  Find the difference between the two answers in Points 1 and 2,
4.  Square the answer to Point 3,
5.  Subtract 75 from your answer in Point 4,
6.  Find the square root of your answer in Point 5,
7.  Multiply your answer in Point 6 by 10.

What is your final answer?

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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the product of the smallest and largest numbers on this 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 SIX ways of making 110 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 110 by inserting 6, 7, 8 and 10 into the gaps on both lines?

•  (◯+◯)×◯+◯ = 110
•  (◯+◯)×◯+double◯ = 110

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Last chance to get all seven correct. Be careful as there may be one or two tricky ones!

1.  (1 – 2) – (3 – 4) = ?
2.  4 ÷ 0.5 = ?
3.  What is 25 less than the product of 20 and 10?
4.  How do you write “Six and six hundredths” in decimal format?
5.  4,000 × 0.02 = ?
6.  Find 10% of £13.
7.  What is 31 × 15?

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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the sum of the odd 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 FIVE ways of making 109 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 109 by inserting 3, 8, 10 and 12 into the gaps on both lines?

•  ◯×◯–(◯+◯) = 109
•  ◯×◯+◯+◯ = 109

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Here’s seven more mental arithmetic questions to try.  Can you get all seven correct?

1.  (11 – 5) – (4 + 1) = ?
2.  What is 10 more than –4?
3.  47 × 4 = ?
4.  0.32 ÷ 4 = ?
5.  3/4 × 2/3 = ?
6.  Which one is bigger: 2 cubed or 3 squared?
7.  You wish to buy two £30 items. Which offer would give you the best deal: (A) 15% off both items, (B) 2nd item is 40% off, (C) get 1/3 off the 2nd item, (D) 25% off 1st item, 10% off 2nd item.

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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

From the list, find TWO numbers that have a sum of 111.

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 SEVEN ways of making 108 when using Lagrange’s Theorem. Can you find them all?

Can you arrive at 108 by inserting 2, 3, 5 and 11 into the gaps on both lines?

•  ◯²×◯²+◯–◯ = 108
•  ◯×◯²+◯²+◯ = 108

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Here’s seven tricky mental teasers to try:

1.  (18 – 5) – (7 – 17) = ?
2.  128 + 294 = ?
3.  How many seconds are in a quarter-of-an-hour?
4.  How many degrees are in three-quarters of a circle?
5.  (16 – 8) × (13 – 8) = ?
6.  On four consecutive days, you spend £55, £74, £36 and £15. What is the average amount spent per day?
7.  What is 15% of £8?

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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

Which two numbers have a difference of 42?

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

Can you arrive at 107 by inserting 9, 10, 11 and 12 into the gaps on both lines?

•  ◯×◯+◯–◯ = 107   (2 different ways!)
•  ◯×◯+(◯–◯)³ = 107

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Here are seven mental arithmetic questions for you to try:

1.  Which number multiplied by itself gives 196?
2.  What is 50 + 400 + 5?
3.  54 – 45 = ?
4.  If Jo runs 10 miles in one hour, how much further would she get in an extra 15 minutes running at the same rate?
5.  (14 – 3) × (7 + 2) = ?
6.  Which fraction comes next in the list: 1/12, 1/6, 1/4, 1/3, …
7.  How many days equal 6 weeks?

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 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

List FIVE different numbers that total 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 SEVEN ways of making 106 when using Lagrange’s Theorem. Can you find them all?

Can you arrive at 106 by inserting 4, 5, 6 and 7 into the gaps on both lines?

•  ◯²+◯²+◯²+◯ = 106
•  ◯³–(◯+◯)×double◯ = 106

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

How quickly can you correctly answer the following seven questions?

1.  (17 – 4) + (12 – 9) = ?
2.  (3 – 2) – (16 – 16) = ?
3.  What is two-thirds plus three-quarters?
4.  109 + 10 = ?
5.  (3 + 16) + (16 + 9) = ?
6.  (11 – 5) + (4 + 1) = ?
7.  What is the perimeter of a 13cm by 13cm square?

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 & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

Which two numbers in the list are 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 SIX ways of making 105 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 105 by inserting 5, 5, 6 and 10 into the gaps on both lines?

•  ◯×(◯+◯)–◯ = 105
•  ◯²+◯–◯÷◯ = 105

Answers can be found here.

Click Paul Godding for details of online maths tuition.