DAY/DYDD 70:

The Main Challenge

Using the numbers 1, 4 and 6 once each with + – × ÷ available, list the SIX numbers that are mathematically possible to make in the range 20 to 30 inclusive.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

What is the sum of the factors of 100 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 FIVE ways of making 70 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which TWO 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 70 by inserting 2, 5, 6 and 10 into the gaps on each line?

  •  ◯×◯+◯× = 70
  •  ◯×◯+◯×◯² = 70
  •  (◯+◯)×–double◯ = 70

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 69:

The Main Challenge

If the number sequence  5  9  13  17  21 . . .  is continued, which is the only number from the following list that will appear later in the sequence?

35    43    59    67    71    85    95

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Is the sum of the even numbers more than double the sum of the 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 are FOUR ways of making 69 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which TWO numbers are NOT 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 69 by inserting 2, 3, 4 and 7 into the gaps on each line?

  •  ◯²×◯+◯+ = 69
  •  ◯³+(◯+◯)÷ = 69
  •  (◯²+◯)×–double◯ = 69

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 68:

The Main Challenge

Can you arrive at the target number 105 by using the five numbers 1, 2, 3, 4 and 5 exactly once each, and with + – ×  ÷ available?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

What is the difference between the highest multiple of 9 and highest multiple of 11?

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

The Mathematically Possible Challenge

Using 46 and 12 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 68 by inserting 2, 3, 6 and 8 into the gaps on each line?

  •  (◯+◯)×+ = 68
  •  ◯²×(◯+◯+◯) = 68
  •  (◯+◯)×–◯² = 68

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 67:

The Main Challenge

Can you correctly place 0 1 1 2 2 3 4 5 5 8 9 and 9 into the 12 gaps below?

◯  +  ◯   =    3    =   ◯  –  ◯
◯  +  ◯   =    8    =   ◯  ×  ◯
◯  +  ◯   =    1    =   ◯  ÷  ◯

Click Mathelona for details on how to purchase our number puzzle pocket book.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Which two numbers have a difference of 25?

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

The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which FOUR 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 67 by inserting 4, 5, 7 and 8 into the gaps on each line?

  •  ◯×◯+× = 67
  •  ◯²+◯+◯×√ = 67
  •  ◯³+(◯+◯)÷◯ = 67

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 66:

The Main Challenge

When multiplying two numbers together and then adding or subtracting a third number, there are four ways of reaching 60 when the three numbers used in each calculation are in the range 1-9 (which can be repeated).

One way to make 60 is (9×6)+6; can you find the other three?

[Note:  (9×6)+6 and (6×9)+6 counts as just one way.]

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

How many pairs of consecutive numbers are there?

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

The Mathematically Possible Challenge

Using 46 and 12 once each, with + – × ÷ available, which SIX 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 66 by inserting 2, 3, 4 and 9 into the gaps on each line?

  •  (◯×◯+◯)× = 66
  •  (◯×◯–◯)× = 66
  •  ◯²×◯+◯× = 66
  •  ◯³+(◯+◯)²+√◯ = 66

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 65:

The Main Challenge

You must arrive at the target number of 24 by using four unique numbers from 10-19 and with + – × ÷ available to use; one such example being (15×12÷18)+14 = 24.

Can you derive another 4-number combination to make 24?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

How many cube numbers are present?

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

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which FIVE 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 65 by inserting 1, 5, 6 and 8 into the gaps on each line?

  •  (◯+◯–◯)× = 65
  •  ◯×◯+(◯–◯)² = 65
  •  ◯²+(◯+◯)÷◯ = 65
  •  ◯²+◯–◯×◯ = 65

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 64:

The Main Challenge

From the numbers 1-30, eliminate the following:

  • numbers containing the digit 1
  • prime numbers
  • numbers in the 20’s
  • factors of 72

What is the only number that remains?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the sum of the square 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 are TWO ways of making 64 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which are the only TWO numbers it is 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 64 by inserting 4, 6, 8 and 10 into the gaps on each line?

  •  (◯+◯)×(◯–◯) = 64
  •  ◯×(◯+◯–◯) = 64
  •  ◯²×(◯+◯)÷◯ = 64
  •  ◯×(◯–◯)×√◯ = 64

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 63:

The Main Challenge

Which is the only digit not represented when listing the square numbers from 10² to 19²?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Find three different numbers that 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 FOUR ways of making 63 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and 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 63 by inserting 3, 3, 4 and 5 into the gaps on each line?

  •  ◯×◯×◯+ = 63
  •  ◯²×◯–× = 63
  •  ◯×◯×(◯+√◯) = 63

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 62:

The Main Challenge

When listing the five 3-digit cube numbers, all the digits from 1 to 9 are represented, except one. Which digit is missing?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the difference between the two 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 THREE ways of making 62 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which is the ONLY number 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 62 by inserting 2, 4, 6 and 9 into the gaps on each line?

  •  (◯+◯)×◯+ = 62
  •  (◯+◯)×◯– = 62
  •  (◯+◯)×◯+◯² = 62

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 61:

The Main Challenge

Read the information below to find each of these three different numbers:

  •  A is the only 2-digit square number that does not contain any odd digits
  •  B is the only 2-digit prime number with both its digits the same
  •  C is the only 2-digit cube number less than 50

Calculate the sum of A, B and C.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the sum of the even numbers 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 FOUR ways of making 61 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which is the ONLY number it is 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 61 by inserting 3, 5, 8 and 10 into the gaps on each line?

  •  ◯×◯++ = 61
  •  (◯–◯)×◯+ = 61
  •  (◯+◯)×◯+double = 61
  •  (◯+◯)×◯–half = 61

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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