DAY/DYDD 8:

The Main Challenge

The concept behind this challenge is similar to my Mathelona number puzzles, so please feel free to click the link for details of my popular pocket book of challenges.

Insert the numbers 1-12, once each, into the 12 gaps so that all four lines work out:

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the difference between the two square numbers listed?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 8?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which FOUR numbers cannot be made from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable

The Target Challenge

Can you arrive at 8 by inserting 1, 2, 4 and 8 into the gaps on each line?

  •  (²×◯²)÷(◯×◯) = 8  (there are 2 ways)
  •  (◯×◯×◯)÷◯² = 8
  •  ◯×◯÷√(◯×◯) = 8
  •  (◯–◯×◯–◯)³ = 8

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 7:

The Main Challenge

Start with the number 7.  Add 1 to this, then 3, then to that answer add 5, then 7 . . . and keep on adding consecutive odd numbers to the previous total.

What is the first answer you reach that is greater than 100?

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the sum of the multiples of 11?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 7?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which FOUR numbers is it 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 7 by inserting 1, 3, 6 and 10 into the gaps on each line?

  •  ◯+×–◯ = 7
  •  ◯×(+) = 7
  •  –√(+ = 7
  •  (+)²÷(–◯) = 7

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 6:

The Main Challenge

. . . is a Kakuro-type puzzle.  Apart from 98751 (or 9+8+7+5+1), there are FIVE other ways of making 30 when combining and adding together five unique digits from 1-9.  Can you list those five combinations?

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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

List FOUR different numbers that have a sum of 100?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 6?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which is the ONLY number that 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 6 by inserting 1, 2, 3 and 4 into the gaps on each line?

  •  ◯÷◯++◯ = 6
  •  (×)÷(×) = 6
  •  (÷◯–◯)×◯ = 6
  •  (²+²–◯²)÷◯² = 6

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 5:

The Main Challenge

This Octaplus puzzle challenges you to find the values of eight letters, A to H, from the given information below. Each letter is a different whole number in the range 1-50:

  1.  H is a third of F,
  2.  B is half of F,
  3.  D minus F is either 15 or 16,
  4.  One-seventh of D is a whole number and odd,
  5.  E equals H plus D,
  6.  G equals E minus B,
  7.  C is a fifth of G,
  8.  A is equal to 120 minus the sum of the other seven numbers.

Can you find the value of each of the eight letters?

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 & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the difference between the highest and lowest prime numbers?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 5?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which is the ONLY number that is 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 5 by inserting 5, 10, 15 and 20 into the gaps on each line?

  •  (÷◯)+(÷◯) = 5
  •  (–◯)×÷◯ = 5
  •  ◯(×÷◯) = 5
  •  ◯(–◯)²÷◯ = 5  (there are 2 ways)
  •  √[(×÷◯)–◯] = 5

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 4:

The Main Challenge

If you allocate each letter of the English alphabet a numerical value as follows: A=1 B=2 C=3 . . . Z=26, the value of the word ‘CAT’ would be 24, simply calculated by doing 3+1+20.

Following this rule, what is the value of the word ‘PUZZLED‘?

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 & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the sum of the multiples of 6?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 4?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 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 4 by inserting 1, 3, 5 and 7 into the gaps on each line?

  •  (+)(+) = 4
  •  (+)÷(×) = 4
  •  √(×–◯×◯) = 4
  •  (◯–◯)×(◯–◯) = 4
  •  (◯²×◯+◯)÷◯ = 4  (there are 2 ways)

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 3:

The Main Challenge

Using 2, 5 and 6 just once each, with + – × ÷ available, which are the only THREE target numbers from 20-30 inclusive that are mathematically possible to achieve?

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 & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

List THREE different numbers that total 100.

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 3?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which FIVE 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 3 by inserting 1, 4, 6 and 8 into the gaps on each line?

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

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 2:

The Main Challenge

Using the numbers on a traditional clock face, 1 to 12, find the following number:

  •  it is half of one of the numbers on the clock face,
  •  it is also two-thirds of another number on the clock face,
  •  . . . and three-quarters of another!

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 & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the total when adding together the prime numbers and square numbers?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 2?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which are the only TWO 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 2 by inserting 2, 3, 5 and 7 into the four gaps on each line?

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

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 1:

The Main Challenge

You’re playing Roll3Dice and have rolled the numbers 1, 2 and 4 with your three dice.

This is a truly unique combination, being the only one where you can make ALL ten target numbers from 1-10, using + – × ÷ as seen below.

Can you place 1, 2 and 4 into the three gaps on each line so all ten calculations work out?

  •  ◯–(◯+◯)  =  1
  •  ◯×◯–◯  =  2
  •  ◯÷◯+◯  =  3
  •  ◯×(◯–◯)  =  4
  •  ◯+◯–◯  =  5
  •  ◯×◯+◯  =  6
  •  ◯×◯–◯  =  7
  •  ◯×◯×◯  =  8
  •  ◯×◯+◯  =  9
  •  ◯×(◯+◯)  =  10

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The 1st & 2nd rows contain the following fourteen numbers:

2   8   9   14   15   17   22   28   40   48   55   63   64   72

What is the sum of all the multiples of 5?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group that CANNOT make 1?

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

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which THREE 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 1 by inserting 2, 4, 6 and 8 into the four gaps on each line?

  •  (+◯)÷(◯+◯) = 1
  •  (◯×◯)÷(◯+◯) = 1
  •  (◯–◯)–(◯÷◯) = 1
  •  (◯+◯–◯)÷◯ = 1
  •  ◯²÷(◯+◯+◯) = 1

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 366:

The Main Challenge

You are playing Roll3Dice and have just rolled 2, 5 and 6 with your three dice.

Using these three numbers once each, with + – × ÷ available, it is possible to make SEVEN target numbers in the range 1-10, as indicated below.

Can you place 2, 5 and 6 into the gaps on each line so that all seven calculations work out?

  •   ◯+◯–◯  =  1
  •   ◯–◯÷◯  =  2
  •   ◯+◯–◯  =  3
  •   ◯×◯–◯  =  4
  •   ◯×◯–◯  =  7
  •   ◯+◯÷◯  =  8
  •   ◯+◯–◯  =  9

For full details, visit Roll3Dice.com or the hashtag #Roll3Dice.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The Bottom-Left to Top-Right diagonal contains the following seven numbers:

3     9     25     27     33     64     81

Another 2-part challenge for the final day of the year:

Part 1: How many of the listed numbers are neither square numbers nor cube numbers?

Part 2: Use these seven numbers exactly once each, with + – × ÷ available to use in your calculation, to arrive at our favourite target number of 7.

The Factors Challenge

Which THREE numbers below are factors of 366?

2     3     4     5     6     7     8     9

The Mathematically Possible Challenge

Using 48 and 12 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 366 by inserting 1, 3, 3, 6 and 6 into the gaps below?

  •  (²+(◯–◯)²)×(◯²–◯) = 366

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 365:

The Main Challenge

You have rolled 1, 5 and 6 on your three dice:

Part 1: What is the highest target number in the range 1-30 that is possible to achieve using these three numbers once each, and with + – × ÷ available?

Click on Mathematically Possible to gather more details of our arithmetic and strategy board game.

Part 2: Similar to Part 1, but which whole numbers in the range 1-10 can be made?

Click Roll3Dice to play a simplified version of the arithmetic part at home.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from 2 up to 84.

The Top-Left to Bottom-Right diagonal contains the following seven numbers:

3     22     24     48     49     80     84

Using these seven numbers exactly once each, with + – × ÷ available to use in your calculation, can you arrive at the target number of 100?

The Factors Challenge

Which numbers below are factors of 365?

15   25   35   45   55   65   75   85   95   None of them

The Mathematically Possible Challenge

Using 48 and 12 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 365 by inserting 2, 3, 4, 5 and 6 into the gaps below?

  •  (◯²×+◯–◯)×◯ = 365

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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