DAY/DYDD/GIORNO/NAP 145:

T he Main Challenge

What is the total of the first SEVEN 3-digit numbers that are NOT multiples of 2 or 5?

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the sum of the multiples of 5?

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

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it’s 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 145 by inserting 3, 4, 5 and 8 into the gaps on each line?

  •  (◯×◯–◯)×◯ = 145
  •  (◯+◯)²–double(◯×◯) = 145
  •  (◯+◯)²+half(◯–◯) = 145

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 144:

The Main Challenge

Another mini-Mathelona challenge where your task is to correctly place the eight digits 1 1 1 2 2 3 4 and 5 into the eight gaps so both lines work out arithmetically:

◯  +  ◯   =    3    =   ◯  –  ◯
◯  +  ◯   =    4    =   ◯  ×  ◯

Click Mathelona for details of our popular pocket book of 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 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

Which five numbers listed can be made by adding two others from the list?

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

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE numbers it’s 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 144 by inserting 4, 6, 9 and 12 into the gaps on each line?

  •  ◯×◯×(◯◯) = 144
  •  ◯×◯×double(◯◯) = 144
  •  ◯×◯×(◯÷◯)² = 144
  •  ◯²×(◯+◯–◯) = 144   (2 different ways!)
  •  ◯×◯+treble(◯×√◯) = 144

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 143:

The Main Challenge

Start with the number 50, then:

+27  42   divide by 5  ×4   +50%   two-thirds of this   ÷7   =    ?

What is your final answer to this 7-step number trail?

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the difference between the highest odd number and lowest 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 FIVE ways of making 143 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the SIX numbers 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 143 by inserting 3, 4, 7 and 10 into the gaps on each line?

  •  (◯+◯)×(◯+◯) = 143
  •  ◯³–◯²×double(◯–◯) = 143

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 142:

The Main Challenge

From the numbers 1-20, eliminate all:

  • square numbers
  • prime numbers
  • triangular numbers
  • multiples of 6

Add together the numbers that remain; what is your total?

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

From this list, 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 FIVE ways of making 142 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only TWO numbers it’s 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 142 by inserting 4, 9, 10 and 13 into the gaps on each line?

  •  ◯×◯+◯×◯ = 142
  •  ◯×◯+◯×√◯ = 142

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 141:

The Main Challenge

One of our easier Mathelona-style challenges, still utilising the four arithmetic operations.  Place the eight digits 1 2 2 3 4 4 5 and 6 into the gaps so both lines work out:

◯  +  ◯   =    6    =   ◯  ×  ◯
◯  –  ◯   =    2    =   ◯  ÷  ◯

If you enjoy this type of number puzzle, click Mathelona for details of our pocket book of 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 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the difference between the two 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 SIX ways of making 141 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 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 141 by inserting 3, 5, 7 and 12 into the gaps on each line?

  •  ◯×(◯+◯)–◯ = 141
  •  (◯×◯+◯)×◯ = 141
  •  ◯³+◯+◯–◯ = 141

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 140:

The Main Challenge

Group the following numbers into three groups of three so that the sum of each of the triples are the same. What is this sum?

11    25    35    43    51    63    73    85    91

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 5th & 7th rows of the playing board contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

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 are FIVE ways of making 140 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 36 and 10 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 140 by inserting 2, 6, 8 and 10 into the gaps on each line?

  •  ◯²+◯²+◯÷◯ = 140
  •  (◯+◯)²–(◯–◯)² = 140
  •  ◯³+◯²–◯×◯ = 140

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 139:

The Main Challenge

There are two sections below, both containing ten letters, A-J.  Each letter is linked to a division calculation:

  • Section 1

D:9÷3  H:8÷2  B:12÷3  I:8÷4  A:4÷2  E:24÷6  G:15÷5  C:20÷4  F:25÷5  J:7÷7

  • Section 2

I:6÷2  G:6÷3  D:10÷2  E:12÷4  J:14÷7  B:20÷5  A:18÷6  C:10÷5  F:16÷4  H:15÷3

Which is the only letter to contain the same answer in both sections?

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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

How many pairs of numbers from the list have a sum of 88?

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 139 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?

1    3    6    10    15    21    28    36    45    55

#TriangularNumbers

The Target Challenge

Can you arrive at 139 by inserting 3, 7, 9 and 11 into the gaps on each line?

  •  ◯×(◯+◯)+◯ = 139
  •  ◯²+◯×◯–◯² = 139

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 138:

The Main Challenge

The two sections below both contain ten letters, A-J; each of which has a multiplication calculation assigned to it:

  • Section 1

C:10×2  J:4×3  F:8×5  D:3×3  I:3×2  G:7×4  B:5×4  H:9×4  E:10×3  A:6×4

  • Section 2

B:12×2  D:6×1  G:8×3  J:5×2  E:6×5  I:6×6  H:8×6  A:9×2  F:7×2  C:6×3

Which is the only letter that contains the same answer in both sections?

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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

Find three different numbers that have a sum 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 are TEN ways of making 138 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?

2    3    5    7    11    13    17    19    23    29

#PrimeNumbers

The Target Challenge

Can you arrive at 138 by inserting 2, 6, 10 and 15 into the gaps on each line?

  •  ◯×◯–◯×◯ = 138
  •  (◯+◯–◯)×◯ = 138
  •  ◯²+double◯+◯+◯ = 138

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 137:

The Main Challenge

It is possible to use seven 5’s (5 5 5 5 5 5 and 5) once each, with the four operations + – × ÷, to make all the target numbers from 1 to 5.

For instance, to arrive at the target numbers 1 and 2, you can do:

  • [(5+5)÷5 – 5÷5] × 5÷5 = 1
  • [(5+5)÷5 – 5÷5] + 5÷5 = 2

Your task is to show how to arrive at the other target numbers 3, 4 and 5.

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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

What is the product of the two prime 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 SIX ways of making 137 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which TWO 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 137 by inserting 4, 5, 6 and 8 into the gaps on each line?

  •  ◯³+◯²+◯×◯ = 137
  •  ◯³+◯×◯÷◯ = 137

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD/GIORNO/NAP 136:

The Main Challenge

Can you arrive at the target number 55 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 containing 49 different numbers, ranging from up to 84.

The 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

What is the sum of the factors of 42?

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

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

13    26    39    52    65    78    91    104    117    130

#13TimesTable

The Target Challenge

Can you arrive at 136 by inserting 4, 6, 7 and 8 into the gaps on each line?

  •  (◯×◯–◯)×◯ = 136
  •  (◯+◯+◯)×◯ = 136

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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