**The Target Challenge**

**The Main Challenge**

One simple rule – multiply two numbers together, then either add or subtract the third number to achieve your target number of **10**. The three numbers used in each calculation must be unique digits from **2-9**.

As an example, one such way of arriving at 10 is by (4×3)–2. Can you find the FIVE other ways of making **10** using this rule?

[Note: (4×3)–2 = 10 and (3×4)–2 = 10 would count as just one way!]

**The 7puzzle Challenge**

The playing board of Buy Soma Online is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

What is the sum of the 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 THREE ways of making **25 **when using *Lagrange’s Theorem*. Can you find them?

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**The Target Challenge**

Can you arrive at **25** by inserting **2**, **5**, **10** and **20** into the gaps on each line?

- ◯²×◯×◯÷◯ = 25
- ◯+◯+◯÷◯ = 25
- ◯÷◯×(◯–◯) = 25

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

Can you arrive at the target answer of **24** by using each of the four numbers **1**, **7**, **13** and **13** exactly once each, and with + – × ÷ available?

**The 7puzzle Challenge**

The playing board of Buy Soma Online is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

Which three different numbers from the list, when added together, make a total 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 is only ONE way of making **24 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

40 41 42 43 44 45 46 47 48 49

#*NumbersIn40s*

**The Target Challenge**

Can you arrive at **24** by inserting **2**, **3**, **6** and **8** into the gaps on each line?

- ◯×◯+◯–◯ = 24
- (◯–◯)²×◯×◯ = 24
- (◯+◯)×◯–◯ = 24

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

To solve this *Octaplus* puzzle, find the values of eight letters, **A to H**, from the given clues. Each letter contains a different whole number in the range **1-50**:

- B minus E is either 14 or 15,
- C is one-quarter of B,
- F is one-seventh of E,
- D is half of B,
- G is H plus C,
- one-third of E is an odd number,
- H is one-third of D,
- A is 150 minus the sum of the other seven numbers.

**The 7puzzle Challenge**

The playing board of Buy Valium Mexico is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

How many square numbers are 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 is only ONE way of making **23 **when using *Lagrange’s Theorem*. Can you find it?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

30 31 32 33 34 35 36 37 38 39

#*NumbersIn30s*

**The Target Challenge**

Can you arrive at **23** by inserting **2**, **3**, **4** and **6** into the gaps on each line?

- ◯×◯+◯–◯ = 23
- (◯³–◯×◯)÷◯ = 23
- (◯²+◯)–(◯³+◯²) = 23

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**The Main Challenge**

. . . is a *Kakuro*-type puzzle. As well as **9321** (or 9+3+2+1), there are FIVE other ways of combining and adding together four unique digits from **1-9** to make **15**. Can you list those five ways?

**The 7puzzle Challenge**

The playing board of Buy Soma Online is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

What is the sum of the factors of 60?

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

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which FOUR 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 **22** by inserting **3**, **4**, **5** and **6** into the gaps on each line?

- ◯×◯+◯÷◯ = 22
- ◯×◯+◯–◯ = 22
- ◯²+◯+◯+√◯ = 22

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**T****h****e**** ****Main Challenge**

Which is the lowest whole number that is NOT a multiple of **4**, **5** or **6**, nor a prime number, square number or cube number?

**The 7puzzle Challenge**

The playing board of Buy Valium Mexico is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 2nd & 4th rows contain the following fourteen numbers:

3 8 10 17 28 32 35 44 48 54 55 60 63 64

Which odd number, when 1 is subtracted from it, becomes a prime 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 **21 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which is the ONLY number it is 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 **21** by inserting **3**, **4**, **5** and **6** into the gaps on each line?

- (◯+◯–◯)×◯ = 21
- ◯×◯+√(◯+◯) = 21
- ◯²–(◯×◯÷◯)² = 21

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**T****h****e**** Main Challenge**

Consider all whole numbers from **1 to 60**, then delete the following:

- all prime numbers,
- … and any number that differs by 1 from a prime,
- all square numbers,
- … and any number that differs by 1 from a square,
- all multiples of 5,
- … and any number that differs by 1 from a multiple of 5,
- all multiples of 7,
- … and any number that differs by 1 from a multiple of 7.

One number will remain, what is it?

**The 7puzzle Challenge**

The playing board of Buy Valium Mexico is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the difference between the highest prime number and highest square 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 **20 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO numbers 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 **20** by inserting **1**, **4**, **6** and **8** into the gaps on each line?

- (◯–◯)×(◯–◯) = 20
- (◯÷◯+◯)×◯ = 20
- (◯+◯)×◯–◯ = 20

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**T****h****e Main Challenge**

Only one of the following 3-digit numbers is **divisible by 3**. Which one?

136 139 245 248 353 357 466 469 572 578 680

[Note: If you don’t know the trick on how to work this out, please get in touch.]

**The 7puzzle Challenge**

**2 **up to **84**.

The 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the sum of the multiples of 7?

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

**The Mathematically Possible Challenge**

**5**, **6** and **8 **once each, with + – × ÷ available, which are the only TWO 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 **19** by inserting **1**, **2**, **3** and **4** into the gaps on each line?

- (◯+◯)×◯+◯ = 19
- (◯+◯)×◯–◯ = 19
- ◯²+(◯+◯)×◯ = 19

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**T****h****e Main Challenge**

All nine numbers from **21 to 29 inclusive** must be allocated to a letter below so that each allocated number satisfies the condition given on the line:

- (a) even number,
- (b) factor of 144,
- (c) power of 3,
- (d) prime number,
- (e) digits which differ by 1,
- (f) exactly 3 factors,
- (g) multiple of 7,
- (h) equal to the sum of all its factors (except the number itself),
- (i) 2nd digit is greater than its 1st digit.

But, the numbers **21 to 29** should only appear once each above!

**The 7puzzle Challenge**

**2 **up to **84**.

The 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

Which odd number, when 21 is added to it, becomes a square 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 THREE ways of making **18 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

**5**, **6** and **8 **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 **18** by inserting **2**, **3**, **4** and **6** into the gaps on each line?

- ◯×◯–◯×◯ = 18
- ◯÷◯×◯×◯² = 18
- (◯÷◯)³×√◯÷◯ = 18

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**T****h****e Main Challenge**

Find the answer to this large number trail which involves fourteen arithmetical steps and includes fraction and percentage calculations.

Start with the number **11**, then:

- double it
- 50% of this
- +50
- subtract thirty-five
- ÷2
- +37
- 3/5 of this
- +70
- –2%
- 1/2 of this
- +311
- subtract twenty
- add ten
- ÷7

What is your final answer?

**The 7puzzle Challenge**

**2 **up to **84**.

The 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the difference between the highest multiples of 5 and 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 only TWO ways of making **17 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

**5**, **6** and **8 **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 **17** by inserting **2**, **5**, **6** and **6** into the gaps on each line?

- ◯²–√(◯×◯)–◯ = 17
- ◯²×◯÷◯+◯ = 17
- (◯÷◯+◯)×◯ = 17

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**T****h****e Main Challenge**

What is the sum of the 50 integers (or whole numbers) from **1 through to 50** inclusive?

**The 7puzzle Challenge**

**2 **up to **84**.

The 1st & 7th rows contain the following fourteen numbers:

2 4 9 11 14 15 22 24 27 30 40 70 72 77

What is the sum of the factors of 24 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 only TWO ways of making **16 **when using *Lagrange’s Theorem*. Can you find both?

**The Mathematically Possible Challenge**

Using **5**, **6** and **8 **once each, with + – × ÷ available, which is the ONLY number it is 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 **16** by inserting **3,** **4**, **6** and **8** into the gaps on each line?

- ◯×◯×◯÷◯ = 16
- ◯²–◯×(◯–◯) = 16
- ◯÷◯×³√◯×◯ = 16

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