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The 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 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

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 56 and 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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The 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 Generic Soma Online 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 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 56 and 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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The 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

The playing board of Buy Generic Soma Online 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 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

Using 56 and 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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The 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

The playing board of Buy Generic Soma Online 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 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

Using 56 and 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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The Main Challenge

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

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

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 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

Using 56 and 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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The Main Challenge

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

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 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 56 and 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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The Main Challenge

Your task is to multiply two numbers together and then subtract a third number to achieve the target answer of 7. The three numbers used in each calculation must all be unique digits from 1-9.

For example, one such way of making 7 is (4×3)5. Can you find SIX other ways to make 7?

[Note:  (4×3)5 = 7  and  (3×4)5 = 7  counts as ONE way.]

The 7puzzle Challenge

The playing board of Buy Ambien From China 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 difference between the total of the prime numbers 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 is only ONE way of making 15 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number it is 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 15 by inserting 2, 3, 5 and 6 into the gaps on each line?

•  ◯×◯+◯◯ = 15
•  ◯÷×²×◯ = 15
•  ◯²–(◯+◯)× = 15

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The Main Challenge

Insert the 12 numbers 1 1 2 2 2 3 5 5 6 7 8 and 8 so that all three lines work out arithmetically:

◯  +  ◯   =     6     =   ◯  –  ◯
◯  +  ◯   =    14    =   ◯  ×  ◯
◯  +  ◯    =    5     =   ◯  ÷  ◯

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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 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 difference between the highest and lowest odd 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 is only ONE way of making 14 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number 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 14 by inserting 2, 4, 5 and 5 into the gaps on each line?

•  ◯+◯+◯+√◯ = 14
•  ◯²–(◯+◯+◯) = 14
•  (◯+÷◯)× = 14

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The Main Challenge

Starting from 2, list the first seven even numbers that are NOT multiples of 3, 5 or 7. What is the 7th number in your list?

The 7puzzle Challenge

The playing board of Buy Ambien From China 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 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 TWO ways to make 13 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which THREE 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 13 by inserting 1, 2, 3 and 4 into the gaps on each line?

•  ◯×◯+◯–◯ = 13
•  ◯×(◯+◯)+ = 13
•  (◯²+²+◯)÷◯ = 13

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The Main Challenge

Add together the 7th prime number, the 7th square number, the 7th 2-digit number and the 7th whole number that contains a 7. What is your answer?

The 7puzzle Challenge

The playing board of Buy Ambien From China 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 two numbers listed have a sum of 101?

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 to make 12 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 45 and 10 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 12 by inserting 2, 3, 4 and 6 into the gaps on each line?

•  (◯–◯)×◯×◯ = 12
•  ◯×◯(◯+◯) = 12
•  ◯÷◯×(◯+◯) = 12
•  ◯²–◯×◯÷◯ = 12
•  (◯²+◯³)×◯÷◯ = 12