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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?

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The 7puzzle Challenge

The playing board of Cheap Xanax 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?

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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?

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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

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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.]

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The 7puzzle Challenge

The playing board of Cheap Xanax 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?

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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?

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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

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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!

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The 7puzzle Challenge

The playing board of Cheap Xanax 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?

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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?

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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

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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.

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?

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The 7puzzle Challenge

The playing board of Cheap Xanax 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?

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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?

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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

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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?

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The 7puzzle Challenge

The playing board of Cheap Xanax 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?

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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?

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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

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The Target Challenge

Can you arrive at 16 by inserting 3, 4, 6 and 8 into the gaps on each line?

  •  ◯×◯×◯÷◯ = 16
  •  ◯²–◯×(◯–◯) = 16
  •  ÷◯׳√◯×◯ = 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.]

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The 7puzzle Challenge

The playing board of Buy Valium London Uk 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?

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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?

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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

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The Target Challenge

Can you arrive at 15 by inserting 2, 3, 5 and 6 into the gaps on each line?

  •  ◯×◯+◯◯ = 15
  •  ◯÷ײ×◯ = 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 Cheap Xanax 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?

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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?

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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

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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?

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The 7puzzle Challenge

The playing board of Buy Valium London Uk 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?

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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?

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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

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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?

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The 7puzzle Challenge

The playing board of Buy Valium London Uk 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?

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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?

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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

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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

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The Main Challenge

Today’s task is to arrive at the target number of 7 by using the four numbers 7, 7, 7 and 7 once each. All four arithmetic operations + – × ÷ are available. Can you do it?

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The 7puzzle Challenge

The playing board of Buy Valium London Uk 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

From this list, what is the sum of the square numbers?

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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 to make 11 when using Lagrange’s Theorem. Can you find it?

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The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

#PrimeNumbers

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The Target Challenge

Can you arrive at 11 by inserting 2, 3, 4 and 5 into the gaps on each line?

  •  ◯×◯+◯–◯ = 11
  •  ◯÷◯×◯+◯ = 11
  •  ◯²(◯×(◯+◯)) = 11

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