DAY/DYDD/GIORNO/NAP 29:

The Main Challenge

What is the 7th 2-digit whole number that is both a multiple of 5 AND contains the letter ‘F’ when written in English?

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

How many pairs of numbers have a difference of 24?

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 29 when using Lagrange’s Theorem. Can you find them both?

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which are the only TWO numbers 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 29 by inserting 2, 3, 4 and 5 into the gaps on each line?

  •  (◯+◯)×+◯ = 29   (there are two ways)
  •  ◯×◯×◯+◯ = 29
  •  ◯²+◯×◯–◯ = 29

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 28:

The Main Challenge

Here is an introductory Mathelona challenge taken from the front cover of Volume 1 of my pocket book series.

◯  +  ◯   =    3    =   ◯  –  ◯
◯  +  ◯   =    4    =   ◯  ×  ◯
◯  +  ◯   =    5    =   ◯  ÷  ◯

Can you insert the digits 1 1 1 1 2 2 2 3 3 4 5 and 6 into the 12 gaps above so all three lines work out arithmetically?

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 odd 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 are THREE ways of making 28 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which are the only THREE numbers 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 28 by inserting 2, 4, 6 and 8 into the gaps on each line?

  •  ◯×◯+◯–◯ = 28
  •  ◯×◯÷◯+◯ = 28
  •  ◯×◯+◯×√◯ = 28
  •  ◯×◯+◯÷◯ = 28
  •  (◯+◯)×◯–◯ = 28
  •  (◯+◯)×◯÷◯ = 28
  •  (◯+◯)×+◯ = 28

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 27:

The Main Challenge

Using each of the numbers 2, 2 and 5 exactly once each, with + – × ÷ available, can you find all NINE numbers from 1-20 that are mathematically possible to make?

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

How many more even numbers than odd numbers are listed?

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

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is 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 27 by inserting 3, 3, 4 and 6 into the gaps on each line?

  •  (◯+◯)×◯+◯ = 27
  •  ◯²+◯◯×◯ = 27
  •  ◯×◯+√(◯×◯) = 27
  •  (◯+◯)×◯◯ = 27
  •  (◯²+◯²)×◯÷◯ = 27

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 26:

The Main Challenge

From the numbers 50-100 inclusive, eliminate all multiples of 5, prime numbers, even numbers and multiples of 3. What is the sum of the two numbers that remain?

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 two 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 THREE ways of making 26 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?

70    71    72    73    74    75    76    77    78    79

#NumbersIn70s

The Target Challenge

Can you arrive at 26 by inserting 2, 4, 5 and 8 into the gaps on both lines?

  •  ◯²+(◯×◯÷◯) = 26
  •  (◯+◯)×◯÷◯ = 26
  •  (◯+◯)×◯+◯ = 26

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 25:

The Main Challenge

One simple rule – multiply two numbers together, then either add or subtract the third number to achieve your target number of 10.  The three numbers used in each calculation must be unique digits from 2-9.

As an example, one such way of arriving at 10 is by (4×3)–2.  Can you find the FIVE other ways of making 10 using this rule?

[Note:  (4×3)–2 = 10  and  (3×4)–2 = 10  would count as just one way!]

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 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 THREE ways of making 25 when using Lagrange’s Theorem. Can you find them?

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?

50    51    52    53    54    55    56    57    58    59

#NumbersIn50s

The Target Challenge

Can you arrive at 25 by inserting 2, 5, 10 and 20 into the gaps on each line?

  •  ◯²×◯×◯÷◯ = 25
  •  ◯+◯+◯÷◯ = 25
  •  ◯÷◯×(◯–◯) = 25

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 24:

The Main Challenge

Can you arrive at the target answer of 24 by using each of the four numbers 1, 7, 13 and 13 exactly once each, and with + – × ÷ available?

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 three different numbers from the list, when added together, make a total of 77?

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 24 when using Lagrange’s Theorem. Can you find it?

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?

40    41    42    43    44    45    46    47    48    49

#NumbersIn40s

The Target Challenge

Can you arrive at 24 by inserting 2, 3, 6 and 8 into the gaps on each line?

  •  ◯×◯+◯–◯ = 24
  •  (◯–◯)²×◯×◯ = 24
  •  (◯+◯)×◯–◯ = 24

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 23:

The Main Challenge

To solve this Octaplus puzzle, find the values of eight letters, A to H, from the given clues. Each letter contains a different whole number in the range 1-50:

  1.  B minus E is either 14 or 15,
  2.  C is one-quarter of B,
  3.  F is one-seventh of E,
  4.  D is half of B,
  5.  G is H plus C,
  6.  one-third of E is an odd number,
  7.  H is one-third of D,
  8.  A is 150 minus the sum of the other seven numbers.

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

How many square numbers are listed?

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 23 when using Lagrange’s Theorem. Can you find it?

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?

30    31    32    33    34    35    36    37    38    39

#NumbersIn30s

The Target Challenge

Can you arrive at 23 by inserting 2, 3, 4 and 6 into the gaps on each line?

  •  ◯×◯+◯–◯ = 23
  •  (◯³–◯×◯)÷◯ = 23
  •  (◯²+◯)–(◯³+◯²) = 23

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 22:

The Main Challenge

. . . is a Kakuro-type puzzle.  As well as 9321 (or 9+3+2+1), there are FIVE other ways of combining and adding together four unique digits from 1-9 to make 15.  Can you list those five ways?

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 60?

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 22 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which FOUR 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 22 by inserting 3, 4, 5 and 6 into the gaps on each line?

  •  ◯×◯+◯÷◯ = 22
  •  ◯×◯+◯–◯ = 22
  •  ◯²+◯+◯+√◯ = 22

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 21:

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 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 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

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 20:

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 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

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

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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