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The 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 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 24 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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The 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

The 7puzzle Challenge

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 24 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

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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The 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 Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 24 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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The 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

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 24 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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The 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

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 24 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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The Main Challenge

•  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

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 24 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 121 by inserting 4, 5, 6 and 7 into the gaps on each line?

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

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The Main Challenge

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

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 24 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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The Main Challenge

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

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 24 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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The Main Challenge

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 the missing digit?

The 7puzzle Challenge

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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

Using 24 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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The Main Challenge

Can you place the 12 numbers 1 1 2 2 3 3 4 5 6 7 8 and 10 into the 12 gaps below so all four lines work out arithmetically?

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

The 7puzzle Challenge

The playing board of Order Adipex-P is a 7-by-7 grid containing 49 different numbers, ranging from 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 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 EIGHT ways of making 117 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which FIVE 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 117 by inserting 3, 6, 9 and 12 into the gaps on each line?

•  ◯×◯+◯+◯ = 117
•  ◯²+◯×(◯–◯) = 117   (2 different ways!)