DAY/DYDD 197:

The Main Challenge

There is just one set of three consecutive numbers in ascending order whose sum is less than 50 and follow this sequence:

  •  prime number – cube number – square number

What is the sum of these three numbers?

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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

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).

Show how you can make 197, in SEVEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 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 197 by inserting 1411 and 14 into the gaps on each line?

  •  ◯×(◯+◯)–◯ = 197
  •  (◯+◯)²–(◯×double◯) = 197

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 196:

The Main Challenge

Here’s a 10-step number trail involving the four arithmetical operations, some 3-digit numbers, plus fractions and percentages.

Start with the number 2, then:

  • add three hundred and eighty
  • 292
  • +106
  • 50%
  • 1/2 of this
  • multiply by nine
  • 1/3 of this
  • 7
  • divide by seven
  • +7

What’s your answer?

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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

What is half of the highest even number?

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).

Show how you can make 196, in TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which FOUR 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 196 by inserting 568 and 9 into the gaps on each line?

  •  (◯+◯)×(◯+◯) = 196
  •  (◯+◯)²+(◯×half◯) = 196
  •  (◯+◯)²–(²+half◯) = 196
  •  ◯³+◯–(◯+double◯) = 196
  •  ◯³+◯–(◯²+√◯) = 196

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 195:

The Main Challenge

In this Kakuro-style question, can you list the ONLY way possible to make 16 when adding together five unique digits from 1-9?

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 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

How many pairs of numbers differ by exactly 10?

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).

Show how you can make 195, in TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers

The Target Challenge

Can you arrive at 195 by inserting 5, 8, 13 and 18 into the gaps on each line?

  •  (◯+◯+◯)×◯ = 195
  •  (◯+◯–◯)×◯ = 195

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 194:

The Main Challenge

This is similar in style to the challenges found at our popular Mathelona number puzzle pocket book. Click the link for more details.

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

Can you insert 0 0 1 1 2 3 3 4 and 4 into the nine gaps above so that all three lines work out arithmetically?

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 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

List THREE sets of three different numbers, each having 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).

Show how you can make 194, in ELEVEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which FOUR 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 194 by inserting 6, 8, 10 and 12 into the gaps on each line?

  •  (◯+◯)×◯–◯ = 194
  •  double(◯×◯)+√(◯–◯) = 194

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 193:

The Main Challenge

When playing Mathematically Possible, players must analyse which numbers can (or can’t) be made from the three numbers rolled on their dice.

Full details of our popular board game can be found at MathPoss.com.

Using the numbers 3, 4 and 6, with + – × ÷ available, which THREE of the following target numbers are NOT mathematically possible to achieve?

1   2   3   5   6   7   8   10   12   13   14   18   21   22   24   27   30

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 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

What is the difference between the sum of the multiples of 5 and sum of the multiples of 6?

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).

Show how you can make 193, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which SIX numbers is it possible to make from the list below?

12    24    36    48    60    72    84    96    108    120

#12TimesTable

The Target Challenge

Can you arrive at 193 by inserting 7, 10, 11 and 13 into the gaps on each line?

  •  ◯×(◯+◯)+◯ = 193
  •  ◯²+◯²+◯+◯ = 193

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 192:

The Main Challenge

This is a number puzzle taken from my scrapbook of brainteasers, a favourite of mine, and used regularly as a mental maths starter in my workshops over the years!

You have a 6-sector dartboard containing the numbers 16, 17, 23, 24, 39 and 40. Your task is to achieve EXACTLY 100 when adding your scores together. This can be done by throwing any number of darts, each of which can land in any sector more than once.

There is only ONE way of achieving a score of 100. How can it be done?

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 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

List two pairs of numbers that differ by 19.

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).

Show how you can make 192, in just TWO different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which are the only TWO numbers is it 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 192 by inserting 4, 6, 8 and 10 into the gaps on each line?

  •  (◯+◯)×(◯+◯) = 192
  •  (◯×◯–◯)×◯ = 192
  •  double(◯×(◯+◯))–◯ = 192

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 191:

The Main Challenge

This is a very special challenge personally endorsed by Robert Sun, inventor of the world-famous maths card game, 24game®.

The idea is very simple; to make 24 from the card below by using the four numbers exactly once each, and with + – × ÷ available.

(The three dots in each corner signifies a hard level of challenge)

Can you also make 24 from the following two combinations using the same rules?

  •  1   5   5   5
  •  4   4   7   7

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 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

What is the sum when adding together all 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).

Show how you can make 191, in FIVE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which THREE 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 191 by inserting 7, 11, 19 and 25 into the gaps on each line?

  •  ◯×◯+◯–◯ = 191
  •  ◯×◯+double(◯–◯) = 191

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 190:

The Main Challenge

This is the 3rd and final part of a number puzzle posted initially on DAY 10, then on DAY 180, and made famous by French writer, George Perec.

The challenge involves using seven 7′s (7, 7, 7, 7, 7, 7 and 7) once each, with + – × and ÷ available, to make various target numbers.

For instance, to make 9 in the previous challenge on DAY 180, you could have done:

  • [7 + (7÷7) + (7÷7)] × (7÷7) = 9

Up until now, it has been possible to make every target number from 1 through to 9 with seven 7’s, so for today’s time-consuming task:

Part 1:  Show how to make all target numbers from 10 through to 19.

Part 2: Which is the first number after 19 that is impossible to make with seven 7’s?

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 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

Which two numbers have a difference of 13?

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 190, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which SIX numbers is it 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 190 by inserting 4, 5, 6 and 14 into the gaps on each line?

  •  (◯+◯)×(◯+◯) = 190
  •  (◯×◯+◯)×◯ = 190
  •  ◯²–◯×(◯–◯) = 190

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 189:

The Main Challenge

Can you insert the numbers 1-9, exactly once each, into the gaps below so that all three lines work out arithmetically?

◯   +   ◯   =   ◯
◯   –   ◯   =   ◯
◯   ÷   ◯   =   ◯

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 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

Which number, when 20 is added to 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 189, in ELEVEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which SIX 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 189 by inserting 3, 4, 5 and 7 into the gaps on each line?

  •  ◯×◯×(◯+◯) = 189
  •  (◯+◯–◯)³+◯³ = 189

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 188:

The Main Challenge

Try the following number challenge similar to the ones found in our Mathelona pocket book of challenges. Click the link for details.

Your task is to make all four lines below work arithmetically by placing the following 16 digits into the 16 gaps.

0    0    1    1    2    2    4    4    5    5    6    6    7    7    8    9

◯  +  ◯   =    15    =   ◯  +  ◯
◯  +  ◯   =     2     =   ◯  –  ◯
◯  +  ◯   =     8     =   ◯  ×  ◯
◯  +  ◯   =     1     =   ◯  ÷  ◯

It’s tricky – but can you do it?

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 2nd & 3rd rows contain the following fourteen numbers:

8   13   17   25   28   36   42   45   48   55   63   64   66   80

What is the sum of the multiples of 16?

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 188, in SIX different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 34 and 12 once each, with + – × ÷ available, which THREE 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 188 by inserting 2, 9, 10 and 11 into the gaps on each line?

  •  ◯×◯×◯–◯ = 188
  •  (◯×◯–half◯)×◯ = 188
  •  (◯+◯)×◯–half◯ = 188

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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