DAY 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

Based on our best-selling arithmetic board game.

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 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 TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

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 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 FIVE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

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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DAY 187:

The Main Challenge

A Keith Number, made famous by Mike Keith, is worked out in a not-too-dissimilar way to Fibonacci Numbers. If you like playing around with numbers, have a go at this fun concept.  The first 2-digit Keith Number, 14, is worked out as follows:

  • Try 14: 1+4=5; 4+5=9; 5+9=14 (the total arrives back to the original number).

By following this pattern, can you find the next 2-digit Keith Number?

[Hint: it’s not too far away!]

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 three numbers, when 6 is added to them, each become multiples of 7?

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 187, in NINE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 34 and 12 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 187 by inserting 457 and 9 into the gaps on each line?

  •  (◯×◯×◯)+◯ = 187
  •  ◯²×◯+◯×√◯ = 187

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 186:

The Main Challenge

Here’s another 10-step question involving all four arithmetic operations and all numbers from 1 to 10.

Start with the number 28, then:

  • divide by four
  • multiply by six
  • subtract two
  • add five
  • divide by nine
  • multiply by one
  • add ten
  • divide by three
  • add eight
  • subtract seven

What is your answer?

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 difference between the sum of the multiples of 11 and the sum of the prime numbers?

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 186, in NINE 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 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 186 by inserting 346 and 9 into the gaps on each line?

  •  (◯×◯+◯)×◯ = 186
  •  (◯×◯+double◯)×◯ = 186

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 185:

The Main Challenge

Your task is to arrive at the target answer of 7 by using each of the numbers 0.7, 2, 7 and 10 exactly once each, 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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

How many multiples of 3 are present?

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 185, 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 SEVEN 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 185 by inserting 5, 1520 and 30 into the gaps on each line?

  •  ◯+◯×◯+◯ = 185
  •  ◯×(◯–◯)–half◯ = 185

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 184:

The Main Challenge

Read the following clues to work out which number I am today:

  •  I am a 2-digit number,
  •  Both 3 and 4 divide exactly into me,
  •  My two digits add up to 9,
  •  I am not a square number.

Who 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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which even number, when halved, 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 184, 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 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 184 by inserting 456 and 8 into the gaps on each line?

  •  (◯×◯+◯)×◯ = 184
  •  (◯×◯+half◯)×◯ = 184

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 183:

The Main Challenge

Simply add together the first seven prime numbers and first seven square numbers. What is the total of these 14 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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which three numbers become square numbers when 5 is added to them?

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 183, in SEVEN 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 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 183 by inserting 1, 5, 8 and 14 into the gaps on each line?

  •  (◯+◯)×◯+◯ = 183
  •  half [(◯+◯)²+◯+half◯] = 183

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 182:

The Main Challenge

Can you place the 12 digits 0, 1, 1, 2, 3, 4, 5, 5, 6, 7, 9 and 9 into the gaps below so that all three lines work out arithmetically?

◯  +  ◯    =     4     =   ◯  –  ◯
◯  +  ◯    =    18    =   ◯  ×  ◯
◯  +  ◯    =     7     =   ◯  ÷  ◯

To order a pocket book full of these popular number puzzles, click 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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

Which two numbers, when each is doubled, become cube numbers?

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 182, 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 THREE target 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 182 by inserting 2, 6, 7 and 14 into the gaps on each line?

  •  (◯×◯+◯)×◯ = 182   (2 different ways!)
  •  (◯+◯)×◯×half◯ = 182

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 181:

The Main Challenge

Your task is to arrive at the target numbers 66, 77, 88 and 99 by using the five numbers 1, 2, 3, 4 and 5 once in each calculation, 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 4th & 7th rows contain the following fourteen numbers:

3   4   10   11   24   27   30   32   35   44   54   60   70   77

What is a quarter of the highest multiple of 10?

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 181, 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 are the FIVE target numbers it is 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 181 by inserting 8, 9, 10 and 11 into the gaps on each line?

  •  ◯×(◯+◯)+◯ = 181
  •  ◯×(◯+◯)–◯ = 181

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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