**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which THREE numbers are possible to make from the list below?

7 14 21 28 35 42 49 56 63 70

#*7TimesTable*

**The Target Challenge**

**T****he Main Challenge**

Using each of the four numbers **0.8**, **0.9**, **1.5** and **5** once each, and with the four arithmetical operations + – × ÷ available to use, can you arrive at the target answer of **7**?

**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 & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

What is the sum of the prime 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 SEVEN ways of making **82 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which THREE numbers are 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 **82** by inserting **1**, **8**, **9** and **10** into the gaps on each line?

- ◯×◯–◯×◯ = 82
- ◯²+◯+◯–◯ = 82
- ◯×◯+√◯–√◯ = 82
- ◯×◯×◯+◯ = 82

**A****nswers **can be found **here**.

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

**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**.

**Sp****read 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**

**Th****e ****Main Challenge**

Carry out the following 15-step number trail – with no calculator!

Start with **20**, then:

+1 ÷3 ×5 –7 +2 ÷6 +4 –1 ×3 ÷4 +4 –5 ×1 +3 ×6 = **?**

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 2nd & 3rd rows contain the following fourteen numbers:

8 13 17 25 28 36 42 45 48 55 63 64 66 80

Which three 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 SIX ways of making **81 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which TWO numbers are 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 **81** by inserting **2**, **3**, **6** and **9** into the gaps on each line?

- ◯×◯×◯÷◯ = 81
- ◯²×◯×◯÷◯ = 81
- ◯²+◯×(◯+◯) = 81

**A****nswers **can be found **here**.

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

**Th****e Main Challenge**

Each of the nine letters, **A-I**, in the two sections below has a subtraction calculation attached to it. Which is the only letter that has the same answer in both sections?

- Section 1

C:24–13 G:14–6 D:20–10 E:15–7 I:14–9 F:18–11 B:9–2 A:17–5 H:25–12

- Section 2

I:16–3 A:15–1 H:20–8 C:19–9 G:12–4 E:11–5 F:21–6 D:14–7 B:27–18

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

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

What is the difference between the highest and lowest multiples of 4?

**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 TWO ways of making **80 **when using *Lagrange’s Theorem*. Can you find them both?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which FOUR numbers is it 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 **80** by inserting **4**, **5**, **8** and **10** into the gaps on each line?

- ◯×◯+◯×◯ = 80
- ◯×◯×(◯–◯) = 80
- ◯×◯×(◯–◯)² = 80
- (◯–◯)×(◯–◯)² = 80
- ◯³+◯×◯÷◯ = 80

**An****swers **can be found **here**.

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

**T****he 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?

**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 & 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?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which FOUR numbers is it 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 **79** by inserting **2**, **5**, **9** and **10** into the gaps on each line?

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

**An****swers **can be found **here**.

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

**T****he 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?

**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 & 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?

**The Mathematically Possible Challenge**

Using **2**, **3** and **11 **once each, with + – × ÷ available, which FOUR numbers is it 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 **78** by inserting **2**, **4**, **5** and **8** into the gaps on each line?

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

**An****swers **can be found **here**.

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

**T****h****e 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

**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 & 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?

**The Mathematically Possible Challenge**

Using **4**, **6** and **12 **once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

2 3 5 7 11 13 17 19 23 29

#*PrimeNumbers*

**The Target Challenge**

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

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

**An****swers **can be found **here**.

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

**T****h****e 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**?

**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 & 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?

**The Mathematically Possible Challenge**

Using **4**, **6** and **12 **once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

70 71 72 73 74 75 76 77 78 79

#*NumbersIn70s*

**The Target Challenge**

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

**A****nswers **can be found **here**.

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

**T****h****e 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?

**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 & 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?

**The Mathematically Possible Challenge**

Using **4**, **6** and **12 **once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1 4 9 16 25 36 49 64 81 100

#*SquareNumbers*

**The Target Challenge**

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

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

**A****nswers **can be found **here**.

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

**T****h****e 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?

**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 & 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?

**The Mathematically Possible Challenge**

Using **4**, **6** and **12 **once each, with + – × ÷ available, which THREE numbers are not possible to make from the list below?

12 24 36 48 60 72 84 96 108 120

#*12TimesTable*

**The Target Challenge**

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

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

**A****nswers **can be found **here**.

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