DAY/DYDD 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

Using 34 and 12 once each, with + – × ÷ available, which THREE numbers are not 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/DYDD 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

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/DYDD 185:

The Main Challenge

Your task is to arrive at the target answer of 7 when 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 NINE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

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/DYDD 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

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/DYDD 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

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/DYDD 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 TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

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/DYDD 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

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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DAY/DYDD 180:

The Main Challenge

This is a continuation of a number puzzle, posted on DAY 10, made famous by French writer, George Perec.

In that challenge, we asked you to use seven 7’s (7, 7, 7, 7, 7, 7 and 7) once each, with + – × and ÷ available, to make target numbers from 1 to 3.

To continue the puzzle, and make 4, you could simply do:

  •  7 – 7÷7 – 7÷7 – 7÷7  =  4

We now invite you to make all the target numbers from 5 through to 9.

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 & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which multiple of 8, when 7 is subtracted from 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 180, in TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which is the ONLY target number 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 180 by inserting 4, 6, 8 and 10 into the gaps on each line?

  •  (◯+◯+◯)×◯ = 180
  •  (◯+◯)×(◯+◯) = 180
  •  ◯²+◯×(◯+◯) = 180
  •  (◯+◯+double◯)×◯ = 180

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 179:

The Main Challenge

You must make all three lines work out arithmetically by inserting the twelve digits 0 1 1 2 2 3 4 4 5 6 8 and 8 into the gaps below:

◯  +  ◯   =    6    =   ◯  –  ◯
◯  +  ◯   =    8    =   ◯  ×  ◯
◯  +  ◯   =    2    =   ◯  ÷  ◯

If you enjoy this, click Mathelona for further details of our number puzzle pocket book.

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 & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

List two sets of three different numbers that both have a total of 77.

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

The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which THREE target 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 179 by inserting 5, 6, 7 and 22 into the gaps on each line?

  •  (◯+◯)×◯+◯ = 179
  •  (half◯)²+10×◯+◯–◯ = 179

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 178:

The Main Challenge

Can you arrive at the target answer of 7 by using each of the numbers 0.2, 0.5, 2 and 2.5 exactly once each, 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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

What is the sum of the factors of 36?

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 178, in TWELVE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which SEVEN target numbers from the list below can be made?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 178 by inserting 10, 11, 16 and 20 into the gaps on each line?

  •  ◯×◯+◯÷◯ = 178
  •  ◯×◯+double(◯–◯) = 178

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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