DAY 173:

The Main Challenge

When allocating each letter of the English alphabet a numerical value as follows; A=1 B=2 C=3 … Z=26, the value of the word SUM, for example, would be 19+21+13 = 53.

What would be the value of our popular number puzzle, 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Find three pairs of numbers that have a sum that is also on the list.

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 173, in SEVEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers

The Target Challenge

Can you arrive at 173 by inserting 5, 7, 14 and 15 into the gaps on each line?

  •  (◯×◯)+(◯×◯) = 173
  •  ◯×(◯+◯)–half◯ = 173

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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WELCOME

A warm Welsh ‘Croeso’ to 7puzzleblog.com and our compendium of daily number puzzles.

Five challenges are posted each day, 7 days a week; designed for our many followers from over 160 countries & territories throughout the world.

As well as our ever-expanding website of arithmetical challenges, this is also the place to learn about our exciting and successful venture into online maths tuition.

The World’s #1 Daily Number Puzzle Website

Type daily number puzzles into Google, Bing or Yahoo and you’ll see 7puzzleblog.com officially listed at #1. We appreciate and value your continued support.

Our aim

. . . is to improve basic knowledge and confidence of arithmetic in a fun way. Start your numerical adventure by trying to solve our latest number puzzles.

How to use our website

As well as our most recent challenges, simply access the remainder of our number puzzles by continually scrolling down or by choosing a particular month listed at the top right hand side of this page.

Alternatively, you can type into the address bar:

  •  7puzzleblog.com/1 for DAY 1, through to . . .
  •  7puzzleblog.com/366 for DAY 366

if you wish to retrieve any individual day’s challenges from the past 12 months.

The Challenges

Five number puzzles are now posted each day, thus adding to our already vast collection of challenges. The daily categories are:

The Main Challenge – involving different types of number puzzle gathered from all parts of the globe, including many of our own creations, and will vary in content and difficulty from one day to the next.

The 7puzzle Challenge – linked to our signature puzzle board game, this is generally the easiest of the five daily number puzzles. Great for younger or less-confident students in improving their knowledge of mathematical terminology.

The Lagrange Challenge – named after the French-Italian mathematician who proved that every positive whole number can be made from adding together up to four square numbers. A medium-difficulty challenge where our puzzlers have to try and arrive at that particular day’s target number using Lagrange’s Theorem.

The Mathematically Possible Challenge – based on our best-selling arithmetic board game and designed to encourage creative number work. Challenges are also at the medium level of difficulty, but may take the longest time to solve. Can you find the possible answer(s)? Requires perseverance!

The Target Challenge – hardest of the challenges, puzzlers must insert the given numbers into the correct places to arrive at the day’s target number. Can sometimes be tricky but will satisfy greatly when solved. A knowledge of BIDMAS, indices and estimation are desirable, but it also helps to think logically and have lots of patience.

Copyright

We always encourage our number puzzles to be printed out for educational purposes in schools, even at home or work, but no part of this website may be republished or transmitted without prior permission.

Puzzles & answers; copyright © Paul Godding.

Spread the message

We’d really appreciate it if you could inform family, friends, students and colleagues about our fabulous daily number puzzles at 7puzzleblog.com. Please tell them there is no fee or registration required, but most importantly answers are provided!

You can get in touch by sending tweets to @7puzzle and e-mails to paul@7puzzle.com.

We hope you enjoy your visit.

Author, Paul Godding

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DAY 172:

The Main Challenge

You are playing our Mathematically Possible board game and have rolled the numbers 6, 6 and 6 with your three dice.  Using these once each, with + – × and ÷ available, which SIX target numbers from 1-30 is it possible to make?

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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

What is the difference between the sum of the multiples of 7 and the sum of the multiples of 9?

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

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the SIX target numbers it’s 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 172 by inserting 3, 4, 5 and 8 into the gaps on each line?

  •  (◯+◯×◯)×◯ = 172
  •  (◯+◯)²+◯²+◯ = 172

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 171:

The Main Challenge

You have the same starting number and final answer, both 22.  There are 10 arithmetical steps altogether but the 10th, and final, step is missing.  If this final step involves a whole number, what should it be to make the final answer 22?

+2   ÷6   ×4   3   ×2   +4   ÷5   +6   ×2   ?   =   22

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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

List three sets of three numbers that all have a sum of 100. The three numbers in each set must be different.

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

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO target numbers it’s 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 171 by inserting 3, 69 and 10 into the gaps on each line?

  •  ◯×◯×◯–◯ = 171
  •  (◯+◯+◯)×◯ = 171

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 170:

The Main Challenge

Study the seven clues and place the numbers 1-9 into the nine positions on this 3-by-3 grid. Each number should appear exactly once:

x              x              x

x              x              x

x              x              x

Clues:

  1.  The 8 is directly above the 5,
  2.  The 6 is further right than the 7,
  3.  The 7 is further right than the 1,
  4.  The 1 is lower than the 5,
  5.  The 5 is further right than the 9,
  6.  The 3 is higher than the 9 and further right than the 2,
  7.  The 4 is higher than the 7 and further right than the 8.

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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the difference between the sum of the highest and lowest even numbers and the product of the highest and lowest even 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 170, in TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which is the ONLY target number it’s 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 170 by inserting 9, 10, 20 and 20 into the gaps on each line?

  •  ◯+◯×◯–◯ = 170
  •  (◯–◯÷◯)×◯ = 170

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 169:

The Main Challenge

Three unique digits from 1-9 must be used to arrive at the target number 18 when multiplying two of these numbers together and adding or subtracting the third unique number, (a×b)±c.

One way of arriving at 18 is (5×4)2.  Find the other FOUR ways it is possible to make 18.

[Note:  (5×4)–2 = 18 and (4×5)2 = 18  counts as just ONE way.]

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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Which number above 20 becomes a multiple of 11 when 20 is subtracted from it?

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

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the only FOUR numbers it’s 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 169 by inserting 1, 3, 13 and 15 into the gaps on each line?

  •  ◯×(◯+◯–◯) = 169
  •  (◯–◯)²+(◯÷◯)² = 169

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 168:

The Main Challenge

The two sections below both contain eight letters, A-H. Each letter has an addition calculation attached, all involving 2-digit numbers.

Which is the only letter that has exactly the same answer in both sections?

  • Section 1

D:68+18   B:51+14   E:47+31   H:62+32   A:44+29   G:59+25   C:36+23   F:38+26

  • Section 2

E:64+28   A:31+27   F:34+22   B:43+19   G:48+36   C:54+16   D:48+21   H:50+38

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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Which three different numbers have a total which is also present on the list?

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 168, in FOUR different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO numbers it’s 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 168 by inserting 2, 4, 6 and 9 into the gaps on each line?

  •  (◯–◯)×◯×◯ = 168
  •  ◯³×◯–◯²×◯ = 168

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 167:

The Main Challenge

Find the sum of all the numbers between 5 and 25 that are divisible by 3, 4 or 7.

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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Which number, when 4 is subtracted from it, becomes a multiple of 15?

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 167, in FOUR different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO numbers it’s 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 167 by inserting 8, 9, 10 and 15 into the gaps on each line?

  •  ◯×◯+◯+◯ = 167
  •  ³√◯×◯²+◯–◯ = 167

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 166:

The Main Challenge

This number trail has seven arithmetical steps.  Start with the number 49, then:

√      add nineteen      50% of this      2      +26      subtract nine      ÷7      =      ?

What is your final 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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the sum of the factors of 24?

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

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the only THREE numbers it’s 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 166 by inserting 4, 7, 14 and 17 into the gaps on each line?

  •  (◯×◯)+(◯×◯) = 166
  •  (◯+◯)²+◯+double◯ = 166
  •  ◯×(◯+◯)–(◯+50%) = 166

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 165:

The Main Challenge

In this Kakuro-type question, can you list the only THREE ways of making 18 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 of 49 different numbers, ranging from up to 84.

The 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

What is the sum of the factors of 120?

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

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and 10 once each, with + – × ÷ available, which are the SIX numbers it’s 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 165 by inserting 5, 10, 15 and 20 into the gaps on each line?

  •  (◯+◯)×◯+◯ = 165
  •  (◯+◯)×◯–◯ = 165

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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