**T****he Factors Challenge**

**The Main Challenge**

Here’s a crafty **Mathelona**-style challenge where your task is to make all three lines work out arithmetically by placing digits from **0 to 5 **into the 12 gaps, with each digit being inserted exactly twice:

◯ + ◯ = 0 = ◯ – ◯

◯ + ◯ = 8 = ◯ × ◯

◯ – ◯ = 2 = ◯ ÷ ◯

Details of our pocket book challenges can be found by clicking **Mathelona**.

**T****he**** 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 & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

What is the sum of the multiples of 10?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

11 22 33 44 55 66 77 88 99 110

#*11TimesTable*

**The Target**** Challenge**

Can you arrive at **270** by inserting **3**, **5**, **6**, **9** and **10** into the gaps on each line?

- (◯×◯×◯)÷(◯–◯) = 270
- (◯+◯+◯)×(◯+◯) = 270
- (◯×◯–◯÷◯)×◯ = 270

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

A warm Welsh ‘Croeso’ to **7puzzleblog.com** and our compendium of **daily number puzzles**.

Five challenges are posted each day, **7 days a week**. These are designed for our many followers from over 160 countries & territories throughout the world.

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

**The World’s #1 Daily Number Puzzle Website**

When typing **daily number puzzles** into *Google*,* Bing* or *Yahoo, *you’ll see **7puzzleblog.com** officially listed at **#1**.

We appreciate and value your continued support.

**Our aim**

. . . is 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 or by choosing a particular month listed at the top right hand side of this page.

Alternatively, in the address bar you can type:

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

if you wish to retrieve any individual day’s challenges from the past 12 months.

**The Challenges**

We have a vast collection of number puzzles, five of which are posted each day, and the majority are our very own creations.

There are seven categories you will see throughout the year:

**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 in improving 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 will be able to arrive at the target number, but your task is to find the impossible group!

**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 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 …

**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 take the longest time to solve. Requires 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 educational purposes in schools, or even at 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, but most importantly 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**

There is just one set of three consecutive numbers in ascending order whose **sum is less than 50** and follow this sequence:

- square number – triangular number – prime number

Can you list this set of three numbers?

**T****he**** 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 & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

Which three different numbers have a sum of exactly 100?

**T****he Factors Challenge**

Which of the following numbers are factors of **269**?

3 5 7 9 11 13 None of them

[ *Hint: Use the ‘bus stop’ method of division to see if any of the above numbers divide exactly into 269 *]

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which are the FIVE numbers it is possible to make from the list below?

10 20 30 40 50 60 70 80 90 100

#*10TimesTable*

**The Target**** Challenge**

Can you arrive at **269** by inserting **2**, **3**, **5**, **6** and **7** into the gaps below?

- (◯+◯+◯)²+(◯+◯)² = 269

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

**The Main Challenge**

Find the sum of the SEVEN different numbers in the range **65 to 85** that are either multiples of 9, 10, 11 or 12.

**T****he**** 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 & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

What is the difference between the two highest multiples of 3?

**T****he Factors Challenge**

Which of the following numbers are factors of **268**?

2 4 6 8 10 12 14

[ *Hint: Use the ‘bus stop’ method of division to see which of the above numbers divide exactly into 268 *]

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

9 18 27 36 45 54 63 72 81 90

#*9TimesTable*

**The Target**** Challenge**

Can you arrive at **268** by inserting **30**, **60**, **90**, **120** and **150** into the gaps below?

- (◯+◯+◯)–(◯÷◯) = 268

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

**The Main Challenge**

Using all four numbers **1**, **5**, **5** and **10** once each, with + – × ÷ available in each calculation, which **even number** from **2 to 20 inclusive** is impossible to make?

**T****he**** 7puzzle Challenge**

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

The 4th & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

What is the sum of the odd numbers?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

8 16 24 32 40 48 56 64 72 80

#*8TimesTable*

**The Target**** Challenge**

Can you arrive at **267** by inserting **2**, **7**, **9**, **11** and **13** into the gaps below?

- ◯×◯×(◯+◯)–◯ = 267

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

**The Main Challenge**

Using the four numbers **2**, **4**, **7** and **8** once each, with + – × ÷ available, show how you can make the following six target numbers:

8 18 28 38 48 58

**T****he**** 7puzzle Challenge**

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

The 4th & 6th rows contain the following fourteen numbers:

3 5 10 12 18 20 32 33 35 44 49 54 56 60

From the list, which three different numbers have a sum of 77?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target**** Challenge**

Can you arrive at **266** by inserting **1**, **2**, **3**, **4** and **7** into the gaps below?

- (◯²+◯)×(◯+◯)²–◯² = 266

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

**The Main Challenge**

. . . is a typical challenge from the excellent American maths card game, *24game*®.

Using the four numbers **2**, **4**, **4** and **9** once each, with + – × ÷ available, can you arrive at the target number of **24**?

**T****he**** 7puzzle Challenge**

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

The 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

Which two numbers, when 16 is added to them, each become a square number?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which THREE numbers are NOT possible to make from the list below?

6 12 18 24 30 36 42 48 54 60

#*6TimesTable*

**The Target**** Challenge**

Can you arrive at **265** by inserting **2**, **4**, **7**, **8** and **10** into the gaps below?

- (◯²+◯–◯)×(◯÷◯) = 265

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

**The Main Challenge**

Your task is to make the four lines below work out arithmetically.

Simply place the digits **0 to 9** into the 16 gaps, but each digit must only be inserted a maximum of twice in the whole challenge.

◯ + ◯ = 12 = ◯ + ◯

◯ + ◯ = 1 = ◯ – ◯

◯ + ◯ = 5 = ◯ × ◯

◯ + ◯ = 2 = ◯ ÷ ◯

Click **Mathelona** for further details of our popular pocket book challenges.

**T****he**** 7puzzle Challenge**

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

The 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

What is the sum of the multiples of 8?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which are the FOUR numbers it is possible to make from the list below?

5 10 15 20 25 30 35 40 45 50

#*5TimesTable*

**The Target**** Challenge**

Can you arrive at **264** by inserting **2**, **4**, **6**, **7** and **9** into the gaps below?

- (◯+◯)×(◯+◯)×√◯ = 264

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

**The Main Challenge**

One of our popular **Mathelona **challenges awaits you; can you complete this by making all four lines work out arithmetically? Fill the 16 gaps with digits **0 to 9**, but each digit can only be inserted a maximum of twice.

◯ + ◯ = 8 = ◯ + ◯

◯ + ◯ = 8 = ◯ – ◯

◯ + ◯ = 8 = ◯ × ◯

◯ + ◯ = 7 = ◯ ÷ ◯

Further details of our pocket book of challenges can be found by clicking **Mathelona**.

**T****he**** 7puzzle Challenge**

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

The 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

Which three different numbers listed have a sum of 100?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which are the FOUR numbers it is possible to make from the list below?

4 8 12 16 20 24 28 32 36 40

#*4TimesTable*

**The Target**** Challenge**

Can you arrive at **263** by inserting **4**, **5**, **6**, **7** and **8** into the gaps below?

- (◯×◯×◯)+◯²+◯ = 263

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**

**The Main Challenge**

Read the following facts to work out my numerical value:

- I am a 3-digit number less than 200
- I am a multiple of 11
- Add 4 to me and I become a multiple of 5
- All my digits are different

Who am I?

**T****he**** 7puzzle Challenge**

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

The 1st & 5th rows contain the following fourteen numbers:

2 6 7 9 14 15 16 21 22 40 50 72 81 84

How many square numbers are present on the list?

**T****he Factors Challenge**

**The Mathematically Possible Challenge**

Based on our best-selling arithmetic board game.

Using **3**, **7** and **9 **once each, with + – × ÷ available, which are the FOUR numbers it is possible to make from the list below?

3 6 9 12 15 18 21 24 27 30

#*3TimesTable*

**The Target**** Challenge**

Can you arrive at **262** by inserting **2**, **4**, **6**, **8** and **10** into the gaps below?

- ◯×(◯×◯–◯)+◯ = 262

**Answers **can be found **here**.

**Click Paul Godding for details of online maths tuition.**