DAY/DYDD 60:

The Main Challenge

Happy St David’s Day/Dydd Gŵyl Dewi Hapus.

It’s our National Day in Wales today so try our special alphabet number puzzle; probably the hardest you can ever try!

The longest place name in the UK is a small village on the island of Anglesey. When allocating each letter of the English alphabet a numerical value, A=1 B=2 C=3 . . . Z=26 and adding the individual letters, what is the total value of  LLANFAIRPWLLGWYNGYLLGOGERYCHWYRNDROBWLLLLANTISILIOGOGOGOCH?

If you wish to hear it pronounced properly, click the following links and listen to Hollywood actor Michael Sheen and weatherman Liam Dutton.

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which two numbers, when each is tripled, are also on 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 THREE ways of making 60 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and 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 60 by inserting 2, 3, 4 and 7 into the gaps on each line?

  •  (+◯)×(+◯) = 60
  •  (◯–◯)×◯× = 60
  •  ◯²+◯²+◯– = 60
  •  ◯²×◯²+◯– = 60

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 59:

The Main Challenge

Your starting number is 18 and your task is to arrive at the same final answer.  There are ten arithmetical steps from beginning to end, each one involving a whole number, but the 9th (and penultimate) step is missing!  What must it be?

÷2   +3   –8   ×6   +4   –3   ÷5   ×2   ?   ×2   =   18

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

What is the difference between the lowest and highest multiples of 4?

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

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which FOUR 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 59 by inserting 4, 5, 6 and 10 into the gaps on each line?

  •  ◯×+ = 59
  •  ◯²+◯×◯+ = 59
  •  (◯+◯)×◯– = 59

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 58:

The Main Challenge

Starting from 1, find the sum of the first SEVEN whole numbers that do not contain a 3, 5 or 7 as part of their number, nor are multiples of 3, 5 or 7.

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

What is the sum of the multiples 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 58 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?

5    10    15    20    25    30    35    40    45    50

#5TimesTable

The Target Challenge

Can you arrive at 58 by inserting 4, 6, 8 and 10 into the gaps on each line?

  •  ◯×◯–◯÷◯ = 58
  •  ◯²+◯+◯+ = 58
  •  ◯²–√(◯×(◯–◯)) = 58

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 57:

The Main Challenge

Place the 12 numbers 1 1 2 2 3 3 4 4 5 6 7 and 8 into the 12 gaps below so all three lines work out:

◯  +  ◯   =    5    =   ◯  –  ◯
◯  +  ◯   =    9    =   ◯  ×  ◯
◯  +  ◯   =    8    =   ◯  ÷  ◯

Can you complete this Mathelona challenge?

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which four different numbers from the 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 FOUR ways of making 57 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which TWO 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 57 by inserting 3, 4, 6 and 11 into the gaps in both lines?

  •  ◯×◯+◯×◯ = 57
  •  (◯+◯+√◯)× = 57

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 56:

The Main Challenge

Can you place the 12 numbers 0 1 2 2 3 3 4 6 6 7 9 and 9 into the 12 gaps below so that all three lines work out arithmetically?

◯  +  ◯   =     6     =   ◯  –  ◯
◯  +  ◯   =    18    =   ◯  ×  ◯
◯  +  ◯    =    3     =   ◯  ÷  ◯

If you enjoyed trying this puzzle, visit our Mathelona page for further details.

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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

How many triangular numbers are 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 56 when using Lagrange’s Theorem. Can you find it?

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?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 56 by inserting 2, 4, 6 and 8 into the gaps on each line?

  •  ◯×◯+◯×◯ = 56
  •  ◯²+×◯+ = 56
  •  (◯+)×◯–◯ = 56
  •  (◯+)×◯–◯⁴ = 56
  •  ◯×(◯+◯÷◯) = 56
  •  (◯+◯)×(◯–◯)² = 56

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 55:

The Main Challenge

Can You Pass A Simple Math Test? was published in the USA in an attempt to emphasise the importance of adult numeracy skills. It contains five multiple choice questions.

Simply answer a, b, c or d each time:

  1. How many seconds are in 2 hours?   a)8,300  b)7,200  c)3,600  d)9,000
  2. What is (4×5)+(718÷3)?   a)42  b)74  c)23  d)21
  3. Calculate 235×13.   a)3,125  b)3,055  c)3,575  d)3,315
  4. If c+d=d, what must the value of c equal?   a)1  b)0.5  c)0  d)1
  5. Which decimal number is equivalent to 3/5?   a)0.35  b)0.53  c)0.6  d)0.3

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 & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

What is the sum of the 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 55 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

90    91    92    93    94    95    96    97    98    99

#NumbersIn90s

The Target Challenge

Can you arrive at 55 by inserting 2, 5, 10 and 15 into the gaps on each line?

  •  ◯×◯–◯×◯ = 55
  •  (◯+◯)×◯+◯ = 55
  •  (◯+◯)×◯–◯ = 55
  •  (◯–◯)×◯+◯ = 55
  •  (◯–◯)×◯–◯ = 55

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 54:

The Main Challenge

Solve this Octaplus puzzle by finding the values of the eight letters, A to H, from the given clues. Each letter contains a different whole number in the range 1-32:

  1.  D minus B is an even number,
  2.  a third of D is an even number,
  3.  G minus B is either 16 or 17,
  4.  C is half of G, and E is half of C
  5.  H is a third of B,
  6.  D is equal to C plus H,
  7.  F is either 18 or 20,
  8.  A is 120 minus the sum of the other seven numbers.

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 & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which three different numbers from the list 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 FIVE ways of making 54 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

80    81    82    83    84    85    86    87    88    89

#NumbersIn80s

The Target Challenge

Can you arrive at 54 by inserting 2, 5, 8 and 12 into the gaps on each line?

  •  ◯×◯+◯+◯ = 54
  •  ◯×◯+◯–◯ = 54
  •  (◯–◯)×◯–◯ = 54
  •  (³√◯+◯÷◯)×◯ = 54

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 53:

The Main Challenge

From the numbers below, eliminate all square numbers, triangular numbers, multiples of 4 and factors of 70.

1  2  3  4  5  6  7  8  9  10  12  14  15  16  18  20  21  24  25

Which is the only number left remaining?

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 & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

What is the difference between the lowest and highest 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 THREE ways of making 53 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number 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 53 by inserting 4, 4, 5 and 6 into the gaps on each line?

  •  (◯+◯)×◯+◯ = 53
  •  ◯²+◯×◯+◯ = 53
  •  ◯²×◯–(◯+◯) = 53

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 52:

The Main Challenge

List the FIVE 2-digit numbers to have the following attributes:

  •  are not odd numbers,
  •  are not multiples of 3, 4, or 7,
  •  has its digits adding up to more than 10.

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 & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

What is the sum of the factors of 36 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 52 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

60    61    62    63    64    65    66    67    68    69

#NumbersIn60s

The Target Challenge

Can you arrive at 52 by inserting 4, 6, 8 and 9 into the gaps on each line?

  •  ◯×◯–◯÷◯ = 52
  •  ◯²–(◯+√◯×√◯) = 52
  •  ◯²+◯×(◯–◯)² = 52
  •  (√◯×◯+◯)×√ = 52

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 51:

The Main Challenge

Using each of the numbers 0.1, 0.5, 3 and 6 once each, and with the four arithmetical operations available, can you arrive at the target answer of 7 in two different ways?

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 & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which three different numbers have a sum that is also on 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 THREE ways of making 51 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 89 and 10 once each, with + – × ÷ available, which THREE 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 51 by inserting 4, 5, 6 and 7 into the gaps on each line?

  •  (+)×◯+◯ = 51
  •  ◯²+(◯+◯)÷ = 51
  •  ◯×◯++◯ = 51
  •  ◯×(◯+√◯)– = 51
  •  ()²×+◯ = 51

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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