DAY/DYDD 134:

The Main Challenge

Read the following facts to work out my numerical value:

  •  I am a single digit number,
  •  If you add 6 to me I become a 2-digit number,
  •  I am an odd number,
  •  I am not a square number,
  •  I am a factor of 30.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 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 highest prime number and the highest odd 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 134 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE numbers is it 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 134 by inserting 2, 3, 5 and 6 into the gaps on each line?

  •  ◯³+◯×◯÷◯ = 134
  •  (◯+◯)²+◯²+◯² = 134

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 133:

The Main Challenge

Group these ten numbers into five pairs so that the difference between the two numbers in each pair is divisible by 7:

6    17    28    37    45    58    64    78    83    98

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 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

From the list, 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 SEVEN ways of making 133 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE numbers is it 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 133 by inserting 10, 11, 13 and 20 into the gaps on each line?

  •  ◯×◯+◯–◯ = 133
  •  ◯×◯+√(◯–◯) = 133

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 132:

The Main Challenge

The 15 arithmetical steps below include percentage & fraction calculations as well as big additions & multiplications:

Start with the number 28, then:

  •  subtract seventy-five percent
  •  +69
  •  –4
  •  1/2 of this
  •  square root of this
  •  ×15
  •  multiply by one
  •  +80%
  •  –10
  •  add four hundred and sixty-five
  •  subtract three hundred and seventeen
  •  two-thirds of this
  • ×0.5
  •  increase by 10%
  •  decrease by 10%

What is your final answer?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 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

Which of these numbers, when 65 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 SEVEN ways of making 132 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which FOUR 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 132 by inserting 4, 5, 6 and 8 into the gaps on each line?

  •  (◯+◯)×(◯+◯) = 132
  •  (◯×◯–double◯)×◯ = 132

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 131:

The Main Challenge

Can you insert the numbers 0 to 9 exactly TWICE EACH into the gaps below so all five lines work out arithmetically?

◯  +  ◯   =    15    =   ◯  +  ◯
◯  +  ◯   =     5     =   ◯  –  ◯
◯  +  ◯   =    10    =   ◯  ×  ◯
◯  –  ◯   =     2     =   ◯  ÷  ◯
◯  +  ◯   =     9     =   ◯  ×  ◯

If you enjoyed attempting this, click this Mathelona link for details of our slightly easier pocket book challenges.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 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 numbers in the 40’s?

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 131 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which SIX 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 131 by inserting 4, 5, 7 and 9 into the gaps on each line?

  •  ◯×◯×◯–◯ = 131
  •  ◯×◯×√◯+◯ = 131

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 130:

The Main Challenge

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

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

Click Mathelona for details of similar pocket-book challenges.

The 7puzzle Challenge

The playing board of the 7puzzle game 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 sum of the multiples of 8 and 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 TEN ways of making 130 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE 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 130 by inserting 2, 3, 5 and 10 into the gaps on each line?

  •  (◯+◯)×◯×◯ = 130
  •  (◯×◯–◯)×◯ = 130
  •  ◯²+◯²+◯²–◯² = 130

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 129:

The Main Challenge

With the four arithmetical operations + – × ÷ available, use all four numbers 1, 1.5, 3 and 4 once each in your attempt to arrive at the target answer of 7.

The 7puzzle Challenge

The playing board of the 7puzzle game 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 four different numbers from the above 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 SEVEN ways of making 129 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which SIX numbers is it 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 129 by inserting 3, 8, 9 and 12 into the gaps on each line?

  •  ◯²+◯–◯×◯ = 129
  •  ◯×(◯+◯)–√◯ = 129
  •  double◯²+◯÷(◯+◯) = 129

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 128:

The Main Challenge

Using all four decimal numbers 0.4, 0.8, 1.2 and 3.5 once each, and with + – × ÷ available, can you arrive at the target answer of 7?

The 7puzzle Challenge

The playing board of the 7puzzle game 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 two prime 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 is only ONE way of making 128 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 36 and 10 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 128 by inserting 4, 8, 10 and 12 into the gaps on each line?

  •  ◯×◯+◯×◯ = 128
  •  ◯×◯+◯²–◯ = 128
  •  ◯⁴×◯÷(◯+◯) = 128

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 127:

The 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 the 7puzzle game 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 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?

The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45    55

#TriangularNumbers

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

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 126:

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 the 7puzzle game 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

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 125:

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

Full details of our popular arithmetic & strategy board game can be found at it’s own dedicated website.

The 7puzzle Challenge

The playing board of the 7puzzle game 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

#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

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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