DAY 180:

The Main Challenge

This is a continuation of a number puzzle, posted on DAY 10, made famous by French writer George Perec.

In that challenge, we asked you to use seven 7’s (7, 7, 7, 7, 7, 7 and 7) once each, with + – × and ÷ available, to make target numbers from 1 to 3.

To continue the puzzle, and make 4, you could simply do:

  •  7 – 7÷7 – 7÷7 – 7÷7  =  4

We now invite you to make all the target numbers from 5 through to 9.

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which multiple of 8, when 7 is subtracted from it, becomes a square number?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 180, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 36 and 12 once each, with + – × ÷ available, which is the ONLY target 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 180 by inserting 4, 6, 8 and 10 into the gaps on each line?

  •  (◯+◯+◯)×◯ = 180
  •  (◯+◯)×(◯+◯) = 180
  •  ◯²+◯×(◯+◯) = 180
  •  (◯+◯+double◯)×◯ = 180

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 179:

The Main Challenge

You must make all three lines work out arithmetically by inserting the twelve digits 0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 8 and 8 into the gaps below:

◯  +  ◯   =    6    =   ◯  –  ◯
◯  +  ◯   =    8    =   ◯  ×  ◯
◯  +  ◯   =    2    =   ◯  ÷  ◯

If you enjoy this, click Mathelona for further details of 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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

List two sets of three different numbers that both have a total of 77.

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 179, in SIX different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 36 and 12 once each, with + – × ÷ available, which THREE target 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 179 by inserting 5, 6, 7 and 22 into the gaps on each line?

  •  (◯+◯)×◯+◯ = 179
  •  (half◯)²+10×◯+◯–◯ = 179

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 178:

The Main Challenge

Can you arrive at the target answer of 7 by using each of the numbers 0.2, 0.5, 2 and 2.5 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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

What is the sum of the factors of 36?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 178, in TWELVE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 36 and 12 once each, with + – × ÷ available, which SEVEN target numbers from the list below can be made?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 178 by inserting 10, 11, 16 and 20 into the gaps on each line?

  •  ◯×◯+◯÷◯ = 178
  •  ◯×◯+double(◯–◯) = 178

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 177:

The Main Challenge

If you enjoy this, click Mathelona for further details of our number puzzles.

You must make all three lines work out arithmetically by inserting the twelve digits 0, 0, 1, 1, 2, 3, 3, 4, 5, 6, 6 and 7 into the gaps below:

◯  +  ◯   =    7    =   ◯  –  ◯
◯  +  ◯   =    5    =   ◯  ×  ◯
◯  +  ◯   =    6    =   ◯  ÷  ◯

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which two numbers have a difference of 21?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 177, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 36 and 12 once each, with + – × ÷ available, which FOUR target 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 177 by inserting 1, 7, 9 and 11 into the gaps on each line?

  •  ◯×(◯+◯)+◯ = 177
  •  ◯²+(◯–◯)×◯ = 177

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 176:

The Main Challenge

You have been given the task of manually numbering a 100-page document from 1 to 100. What is the total of all the individual digits written?

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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Find three pairs of numbers that each have a sum of 42.

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 176, in TWO different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 36 and 12 once each, with + – × ÷ available, which THREE target 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 176 by inserting 6, 7, 8 and 9 into the gaps on each line?

  •  (◯+◯+◯)×◯ = 176
  •  ◯²+◯²+◯²–treble◯ = 176

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 175:

The Main Challenge

Three people answered four multiple choice problems each, with a choice of A B or C, and their responses are shown here:

  • Tim:    A  B  B  C
  • Tam:   A  C  B  A
  • Tom:   B  B  C  A

If two people answered two questions correctly and one person had them all wrong, can you work out what the correct answers could be?

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 of the square numbers listed has the most number of factors?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 175, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1    3    5    7    9    11    13    15    17    19

#OddNumbers

The Target Challenge

Can you arrive at 175 by inserting 1, 5, 10 and 15 into the gaps on each line?

  •  ◯²+(◯×◯×◯) = 175
  •  ◯²–(◯×◯×◯) = 175
  •  (◯+◯)×◯+double◯ = 175
  •  (◯+◯)×◯+treble◯ = 175

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 174:

The Main Challenge

Read the facts below:

  • I am a 2-digit number,
  • I am a multiple of 7,
  • The difference between my two digits is 4.

Which number am I?

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 number, when 1 is subtracted from it, becomes a square number?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 174, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45    55    66

#TriangularNumbers

The Target Challenge

Can you arrive at 174 by inserting 9, 10, 16 and 20 into the gaps on each line?

  •  (◯+◯)×(◯–◯) = 174
  •  ◯×◯+◯–◯ = 174

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 173:

The Main Challenge

When allocating each letter of the English alphabet a numerical value as follows; A=1 B=2 C=3 … Z=26, the value of the word SUM, for example, would be 19+21+13 = 53.

What would be the value of our popular number puzzle, MATHELONA?

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

Find three pairs of numbers that have a sum that is also on the list.

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 173, in SEVEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers

The Target Challenge

Can you arrive at 173 by inserting 5, 7, 14 and 15 into the gaps on each line?

  •  (◯×◯)+(◯×◯) = 173
  •  ◯×(◯+◯)–half◯ = 173

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 172:

The Main Challenge

You are playing our Mathematically Possible board game and have rolled the numbers 6, 6 and 6 with your three dice.  Using these once each, with + – × and ÷ available, which SIX target numbers from 1-30 is it possible to make?

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 sum of the multiples of 7 and the sum of the multiples of 9?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 172, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the SIX target numbers it’s 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 172 by inserting 3, 4, 5 and 8 into the gaps on each line?

  •  (◯+◯×◯)×◯ = 172
  •  (◯+◯)²+◯²+◯ = 172

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 171:

The Main Challenge

You have the same starting number and final answer, both 22.  There are 10 arithmetical steps altogether but the 10th, and final, step is missing.  If this final step involves a whole number, what should it be to make the final answer 22?

+2   ÷6   ×4   3   ×2   +4   ÷5   +6   ×2   ?   =   22

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

List three sets of three numbers that all have a sum of 100. The three numbers in each set must be different.

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 171, in NINE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO target numbers it’s possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable

The Target Challenge

Can you arrive at 171 by inserting 3, 69 and 10 into the gaps on each line?

  •  ◯×◯×◯–◯ = 171
  •  (◯+◯+◯)×◯ = 171

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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