**The Target Challenge**

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

With the four arithmetical operations + – × ÷ available, use all four numbers **1**, **1.5**, **2** and **6** once each in your attempt to make the target answer of **7**.

**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 64?

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

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**The Target Challenge**

Can you arrive at **127** by inserting **4**, **7**, **8** and **10** into the gaps on each line?

- (◯+◯)×◯+◯ = 127
- ◯²+◯×◯–√◯ = 127
- ◯²+◯+◯+double◯ = 127

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

You have SIX each of **7puzzleland**‘s brand-new **4p** and **7p** coins. Your task is to try and make various amounts from 20p and above with these coins.

As shown here, the first few have been done for you:

**20p**can be made from 5 × 4p coins,**21p**from 3 × 7p coins,**22p**from 2 × 7p coins and 2 × 4p coins . . .

From 20p upwards, what is the lowest amount you CANNOT make from your 12 coins?

**The 7puzzle Challenge**

The playing board of Buy Generic 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 difference between the highest multiple of 11 and lowest multiple 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 EIGHT ways of making **126 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which TWO numbers is it 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 **126** by inserting **2**, **3**, **6** and **9** into the gaps on each line?

- ◯×◯×(◯–◯) = 126
- ◯×(◯×◯–◯²) = 126
- ◯²×◯+◯×◯ = 126
- ◯³×◯–◯²×◯ = 126
- ◯²×◯+double(◯×◯) = 126

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

Using the numbers **3**, **4** and **5** just once each, and with + – × ÷ available, only FOUR of the numbers on the list below are possible to achieve. Which ones are they?

1 3 6 9 10 12 15 18 21 24 27 30

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

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

Which multiple of 5, when subtracting 4 from 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 SEVEN ways of making **125 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** 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 **125** by inserting **5**, **10**, **15** and **20** into the gaps on each line?

- ◯×◯+◯+◯ = 125
- ◯×◯–◯×◯ = 125
- ◯²–◯×(◯–◯) = 125
- (◯+◯)×(◯–◯) = 125
- ◯×◯+◯+double◯ = 125

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

A palindromic number is a number that can be read the same forwards and backwards (e.g. 333 and 797). How many palindromic numbers are there between **100 and 1,000**?

**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 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 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 SIX ways of making **124 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which THREE 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 **124** by inserting **5**, **8**, **10** and **16** into the gaps on each line?

- (◯+◯)×◯+√◯ = 124
- ◯×◯–(◯÷◯)² = 124
- (◯–◯÷◯)×◯ = 124

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

From the numbers **1-30** inclusive, delete:

- multiples of 5
- factors of 36
- numbers containing a ‘7’
- prime numbers
- even numbers

Which is the only number that remains?

**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 three different numbers on the list 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 **123 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which THREE numbers is it 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 **123** by inserting **3**, **9**, **10** and **12** into the gaps on each line?

- ◯×◯+◯÷◯ = 123
- ◯×◯+half(◯×◯) = 123
- (◯+◯)×◯+half◯ = 123

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

Find the sum of the first SEVEN whole numbers that has a **3** or **5** as part of their number OR are multiples of **3** or **5**.

**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 and lowest 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 EIGHT ways of making **122 **when using *Lagrange’s Theorem*. Can you find them all?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which FOUR numbers is it 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 **122** by inserting **2**, **4**, **7** and **10** into the gaps on each line?

- ◯²+◯×(◯+◯) = 122
- (◯+◯)²–double(◯+◯) = 122
- ◯⁴÷◯+double(◯–◯) = 122

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Read the following facts below about a particular number:

- It is a 2-digit number,
- It is an even number,
- When the two digits are added together they make another 2-digit even number that is also a square number.

What is the number?

**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 sum of the multiples of 11 and the sum of the 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 SIX ways of making **121 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **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 **12**1 by inserting **4**, **5**, **6** and **7** into the gaps on each line?

- (◯+◯)×(◯+◯) = 121
- (◯+◯)²×(◯–◯) = 121
- ◯³–◯×(◯–◯) = 121

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Your task is to make the target number of **10** by adding together five numbers. You are limited to using **1 to 5**, but these can be used any number of times in each sum.

One way to make 10 is 5+2+1+1+1 (or 52111); can you find the other FIVE ways?

**The 7puzzle Challenge**

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

The 5th & 6th rows contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the sum of the multiples of 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 just TWO ways of making **120 **when using *Lagrange’s Theorem*. Can you find them both?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which THREE numbers are NOT 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 **120** by inserting **3**, **4**, **5** and **6** into the gaps on each line?

- (◯+√◯)×◯×◯ = 120
- (◯×◯)²×◯÷◯ = 120
- (double(◯+◯)²)×◯÷◯ = 120

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Using the numbers **3**, **6** and **6** just once each, and with + – × ÷ available, which THREE of the following target numbers are NOT mathematically possible to achieve?

1 2 3 4 6 8 9 12 15 18 21 24

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**The 7puzzle Challenge**

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

The 5th & 6th rows contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

Which number, when adding 50 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 FOUR ways of making **119 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

Using **2**, **4** and **12 **once each, with + – × ÷ available, which THREE numbers is it 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 **119** by inserting **2**, **6**, **9** and **11** into the gaps on each line?

- (◯+◯)×(◯–◯) = 119
- ◯×◯×◯+◯ = 119

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Instead of being numbered **1-12**, a traditional clock had **√1**, **√4**, **√9** . . . **√144** around its circumference. Every digit is represented on the clock, except one.

What is this missing digit?

**The 7puzzle Challenge**

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

The 5th & 6th rows contain the following fourteen numbers:

5 6 7 12 16 18 20 21 33 49 50 56 81 84

What is the sum of the factors of 40 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 SEVEN ways of making **118 **when using *Lagrange’s Theorem*. Can you find them?

**The Mathematically Possible Challenge**

**2**, **4** and **12 **once each, with + – × ÷ available, which THREE numbers is it 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 **118** by inserting **1**, **2**, **4** and **5** into the gaps on each line?

- ◯³+◯–◯×◯ = 118
- (◯³–◯×◯)×◯ = 118

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