**The Target Challenge**

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

What is the **7th** 2-digit whole number that is both a multiple of 5 AND contains the letter ‘F’ when written in English?

**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 3rd & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

How many pairs of numbers have a difference of 24?

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

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**The Target Challenge**

Can you arrive at **29** by inserting **2**, **3**, **4** and **5** into the gaps on each line?

- (◯+◯)×◯+◯ = 29 (there are two ways)
- ◯×◯×◯+◯ = 29
- ◯²+◯×◯–◯ = 29

**An****swers **can be found **Buy Discount Phentermine Online**.

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**The Main Challenge**

Here is an introductory Buy Xanax Pills Online challenge taken from the front cover of Volume 1 of my pocket book series.

◯ + ◯ = 3 = ◯ – ◯

◯ + ◯ = 4 = ◯ × ◯

◯ + ◯ = 5 = ◯ ÷ ◯

Can you insert the digits **1 1 1 1 2 2 2 3 3 4 5** and **6** into the 12 gaps above so all three lines work out arithmetically?

**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 3rd & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

What is the sum of the odd numbers 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 **28 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which are the only THREE 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 **28** by inserting **2**, **4**, **6** and **8** into the gaps on each line?

- ◯×◯+◯–◯ = 28
- ◯×◯÷◯+◯ = 28
- ◯×◯+◯×√◯ = 28
- ◯×◯+◯÷◯ = 28
- (◯+◯)×◯–◯ = 28
- (◯+◯)×◯÷◯ = 28
- (◯+◯)×◯+◯ = 28

**A****nswers **can be found **Buy Discount Phentermine Online**.

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**The Main Challenge**

Using each of the numbers **2**, **2** and **5** exactly once each, with + – × ÷ available, can you find all NINE numbers from **1-20** that are mathematically possible to make?

**The 7puzzle Challenge**

The playing board of Buy Phentermine Yellow 30 Mg is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 3rd & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

How many more even numbers than odd 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 are THREE ways of making **27 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **6** and **11 **once each, with + – × ÷ available, which are the only TWO 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 **27** by inserting **3**, **3**, **4** and **6** into the gaps on each line?

- (◯+◯)×◯+◯ = 27
- ◯²+◯–◯×◯ = 27
- ◯×◯+√(◯×◯) = 27
- (◯+◯)×◯–◯ = 27
- (◯²+◯²)×◯÷◯ = 27

**Answers **can be found **Buy Discount Phentermine Online**.

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**The Main Challenge**

From the numbers **50-100** inclusive, eliminate all multiples of 5, prime numbers, even numbers and multiples of 3. What is the sum of the **two numbers** that remain?

**The 7puzzle Challenge**

The playing board of Buy Phentermine Yellow 30 Mg is a 7-by-7 grid containing 49 different numbers, ranging from **2 **up to **84**.

The 3rd & 6th rows contain the following fourteen numbers:

5 12 13 18 20 25 33 36 42 45 49 56 66 80

What is the difference between the two multiples of 10?

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

**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?

70 71 72 73 74 75 76 77 78 79

#*NumbersIn70s*

**The Target Challenge**

Can you arrive at **26** by inserting **2**, **4**, **5** and **8** into the gaps on both lines?

- ◯²+(◯×◯÷◯) = 26
- (◯+◯)×◯÷◯ = 26
- (◯+◯)×◯+◯ = 26

**Answers **can be found **Buy Discount Phentermine Online**.

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**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?

**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?

50 51 52 53 54 55 56 57 58 59

#*NumbersIn50s*

**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

**A****nswers **can be found **Buy Discount Phentermine Online**.

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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**

**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 Phentermine Yellow 30 Mg 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**

**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**

**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**

**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**

**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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