DAY/DYDD 233:

The Main Challenge

Firstly, write down three separate lists only containing numbers in the range 1 to 100:

  •  List 1 – multiples of 9
  •  List 2 – factors of 108
  •  List 3 – triangular numbers

Part 1: Which is the only number present on all three lists?

Part 2: List the eight other numbers that are on exactly two of the lists?

Part 3: How many DIFFERENT numbers are written on the three lists?

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 of the playing board contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

From the list, what is the sum of the even 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 EIGHT different ways to make 233 when using Lagrange’s Theorem. How many of them can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which is the ONLY number 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 233 by inserting 11, 12, 13, 14 and 15 into the gaps below?

  •  6×◯+5×◯+4×◯+3×◯–◯ = 233

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 232:

The Main Challenge

Try the following Mathelona challenge, taken from our pocket book of challenges.

Can you make all three lines work out arithmetically by placing the 12 digits below into the 12 gaps?

0     1     1     2     2     3     3     4     5     6     6     7

◯  +  ◯   =    6    =   ◯  –  ◯
◯  +  ◯   =    9    =   ◯  ×  ◯
◯  +  ◯   =    3    =   ◯  ÷  ◯

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 of the playing board contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

From the list, how many multiples of 9 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 FIVE different ways to make 232 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which are the FOUR numbers 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 232 by inserting 4, 8, 12, 16 and 20 into the gaps below?

  •  ◯×◯–◯×◯÷◯ = 232

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 231:

The Main Challenge

Try the following Mathelona-style challenge, similar to those found in our pocket book, details of which can be found by clicking Mathelona.

0    0    1    2    2    2    2    4    4    5    5    6    6    7    7    8

◯  +  ◯   =     6     =   ◯  +  ◯
◯  +  ◯   =     5     =   ◯  –  ◯
◯  +  ◯   =    12    =   ◯  ×  ◯
◯  +  ◯   =     7     =   ◯  ÷  ◯

Your task is to make all four lines work out arithmetically by placing the 16 listed digits into the 16 gaps.  Can you complete 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 2nd & 4th rows of the playing board contain the following fourteen numbers:

3   8   10   17   28   32   35   44   48   54   55   60   63   64

From the list, find two pairs of numbers that each have a difference of 29.

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 NINE different ways to make 231 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which are the SIX numbers 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 231 by inserting 510, 1520 and 25 into the gaps below?

  •  ◯×◯–◯–◯÷◯ = 231

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 230:

The Main Challenge

Use all three numbers in each of the five groups below, with + – × ÷ available, to try and make the target of 23. But for one of the groups it is impossible. Which one?

  •   1    4    6
  •   2    5    5
  •   3    4    5
  •   3    4    6
  •   3    5    6

Full details of our number & strategy board game, click Mathematically Possible.

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 of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which three different numbers 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 THIRTEEN different ways to make 230 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which is the ONLY number 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 230 by inserting 2, 3, 5, 6 and 7 into the gaps below?

  •  ◯×(◯+◯)²+◯×◯ = 230

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 229:

The Main Challenge

There are five different 24game® challenges below.

For each group of four numbers, your task is to arrive at the target answer of 24 by using each of the four digits exactly once, with + – × ÷ available:

  •   1    2    3    4
  •   2    3    4    5
  •   3    4    5    6
  •   4    5    6    7
  •   5    6    7    8

All five challenges are possible, can you do them all?

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 of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the total when adding together all 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 TEN different ways to make 229 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 24 and once each, with + – × ÷ available, which FIVE 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 229 by inserting 2, 3, 4, 5 and 7 into the gaps below?

  •  ◯²×◯+◯²×◯+◯ = 229

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 228:

The Main Challenge

You have been given a starting number as well as an end answer. There are seven arithmetical steps in all, but the middle step is missing!

Start with the number 7, then:

2    ×4    +1    ?    ×5    ÷3    +2    =    7

The missing step involves a single-digit integer (whole number).  Work out this missing step so the final answer will also be 7.

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 of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which four different numbers above 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 TEN different ways to make 228 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which FOUR 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 228 by inserting 34, 5 and 6 into the gaps on each line?

  •  ◯×(◯²+◯²–◯) = 228
  •  ◯×(◯²×◯+double◯) = 228

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 227:

The Main Challenge

Firstly, allocate each letter of the English alphabet a numerical value as follows: A=1, B=2, C=3 . . . Z=26.  When the values of the individual letters are added together, calculate the total value of our popular maths card game, FlagMath.

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 of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the sum of the square numbers present 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 EIGHT different ways to make 227 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which SEVEN 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 227 by inserting 38, 10 and 15 into the gaps on each line?

  •  (◯+◯)×◯–◯ = 227
  •  (◯+◯)×◯+◯³ = 227 

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 226:

The Main Challenge

Your task is to arrive at the target number of 47 by using all five numbers 1, 2, 3, 4 and 5 exactly once each. Can you arrive at 47 in two different ways?

Remember, you have – × ÷ available to use in both calculations.

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 of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

From the list, how many multiples of 8 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 TWELVE different ways to make 226 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Using 24 and once each, with + – × ÷ available, which FOUR 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 226 by inserting 45, 6 and 7 into the gaps on each line?

    •  ◯×◯×◯+◯² = 226
    •  ◯²×double◯+double(◯+◯) = 226

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 225:

The Main Challenge

Each of the five numbers below is the product of two prime numbers:

15     35     77     143     323

Which is the odd one out, and why?

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 & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the sum of the 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 FOURTEEN different ways to make 225 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

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

15    30    45    60    75    90    105    120    135    150

#15TimesTable

The Target Challenge

Can you arrive at 225 by inserting 345 and 9 into the gaps on each line?

  •  (◯–◯)×◯×◯² = 225   (there are 2 ways!)
  •  (◯+◯+◯–◯)² = 225

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 224:

The Main Challenge

Today’s task is to multiply two numbers together, then either add or subtract the third number to achieve the target answer of 37.

Using the formula (a×b)±c, where a, b and c are three unique digits from 1-9, one way of achieving 37 is (7×5)+2; can you find the other SEVEN ways?

[Note: (7×5)+2 = 37 and  (5×7)+2 = 37 counts 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 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

From the list, which three different numbers 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 is only ONE way to make 224 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 46 and once each, with + – × ÷ available, which is the ONLY number it is 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 224 by inserting 127 and 7 into the gaps on each line?

  •  ◯×◯²×(◯+◯) = 224
  •  ◯⁵×◯³×◯²÷◯ = 224

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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