DAY 318:

The Main Challenge

Using the numbers 2, 5 and 10 once each, with + – × ÷ available, which ELEVEN target numbers from 1-30 are mathematically possible to achieve?

This is a number puzzle associated with our board game, Mathematically Possible, an excellent resource involving mental arithmetic and strategy. Click the above link for details of our excellent board game.

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

3   4   6   12   15   17   20   35   42   63   72   77   80   81

What is the difference between the square roots of the two square numbers shown above?

The Factors Challenge

Which TWO numbers below are not factors of 318?

1      2      3      4      5      6

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

50    51    52    53    54    55    56    57    58    59

#NumbersIn50s

The Target Challenge

Can you arrive at 318 by inserting 1, 2, 4, 9 and 10 into the gaps below?

  •  (◯+◯)²+(◯+◯)²+◯ = 318

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, seven days a week, and designed for our many followers from nearly 170 countries & territories throughout the world.

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

The World’s #1 Daily Number Puzzle Website

When typing daily number puzzles into top search engines such as Google, BingYahoo, Baido, DuckDuckGo and Ecosia, you’ll see 7puzzleblog.com officially listed at #1 each time.

We appreciate and value your continued support.

Our aim

Simply to help improve basic knowledge and confidence of arithmetic in a fun way. Start your numerical adventure by trying to solve today’s five number puzzles.

How to use our website

As well as our latest challenges, simply access the remainder of our number puzzles by continually scrolling down the page.

Alternatively, to retrieve and attempt any particular day’s challenges from the past 12 months, just type in the address bar:

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

The Challenges

We have a vast collection of number puzzles, the majority of which are our very own creations and are in seven categories:

The Main Challenge – involving different types of number puzzle gathered from all parts of the globe 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 and will also improve their knowledge of mathematical terminology.

The Roll3Dice Challenge (DAYS 1 to 10) – puzzlers will be given seven groups of three numbers which replicate the rolling of three dice. The numbers in six of these groups will be able to arrive at the target number, but your task is to find the impossible group!

The Lagrange Challenge (DAYS 11 to 250) – 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 puzzlers must arrive at that particular day’s target number using his theorem.

The Factors Challenge (DAYS 251 to 366) – again related to that particular day’s number, puzzlers have to find which of the numbers listed, if any, are factors of the number in question (it will divide exactly into it). Good practice for ‘bus-stop’ division, and great to test some of the mathematical tricks available to find whether our number is a multiple of 2, 3, 4, 5 . . . and so on.

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 require perseverance to find the possible answers!

The Target Challenge – hardest of the challenges, puzzlers must insert the given numbers into the correct gaps 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 is desirable, but it will also help to think logically.

Copyright

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

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 to access them, but most importantly that 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 317:

The Main Challenge

Here is a number puzzle similar in concept to my FlagMath card game. Many schools are now playing the various editions, so here’s a taster:

Each of the eight letters, A-H, in the two sections contain a calculation with an answer in the 20’s:

  • Section 1

B:84÷4   G:296   C:3515   D:14+10   A:5×5   H:72÷3   E:7×4   F:16+11

  • Section 2

H:15+12   B:348   F:9×3   E:48÷2   C:11×2   G:60÷3   A:17+12   D:4015

Which is the only letter that has the SAME answer in BOTH sections?

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 columns contain the following fourteen numbers:

2   10   13   16   21   22   27   33   45   48   55   56   60   70

How many of the above become prime numbers when 10 is added to them?

The Factors Challenge

Which of the following numbers are factors of 317?

3    5    7    9    11    13    15    17    None of them

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which are the THREE numbers it is possible to make from the list below?

30    31    32    33    34    35    36    37    38    39

#NumbersIn30s

The Target Challenge

Can you arrive at 317 by inserting 7, 8, 9, 10 and 11 into the gaps below?

  •  ◯×◯×◯+◯×◯ = 317

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 316:

The Main Challenge

One from our range of Mathelona number puzzles now available in pocket book format.  Your task is to make all three lines work out arithmetically by filling the 12 gaps with the following numbers:

0     0     1     1     2     2     2     2     4     5     6     7

Can you successfully complete this?

◯  +  ◯   =    6    =   ◯  –  ◯
◯  +  ◯   =    2    =   ◯  ×  ◯
◯  +  ◯   =    7    =   ◯  ÷  ◯

Full details of our pocket book can be found by clicking Mathelona.

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 columns contain the following fourteen numbers:

2   10   13   16   21   22   27   33   45   48   55   56   60   70

What is the sum of the multiples of 11 listed above?

The Factors Challenge

Which is the ONLY number below that is a factor of 316?

3      4      5      6      7      8      9

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which is the ONLY number it is 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 316 by inserting 2, 4, 5, 6 and 7 into the gaps below?

  •  ◯²×◯²–◯×◯×◯ = 316

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 315:

The Main Challenge

Try this 10-step number trail involving the four arithmetical operations and all the numbers from 1 to 10.

Start off with the number 27, then:

  •  divide by 3
  •  subtract 1
  •  multiply by 6
  •  add 2
  •  ÷10
  •  +8
  •  –9
  •  ×4
  •  add 5
  •  ÷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 2nd & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

How many multiples of 5 are listed?

The Factors Challenge

Which TWO of the following numbers are not factors of 315?

3     5     7     9     11     13     15

The Mathematically Possible Challenge

Using 47 and 11 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 315 by inserting 1357 and 9 into the gaps below?

  •  (+)²×double◯+◯×◯ = 315

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 314:

The Main Challenge

Today’s task using the excellent, addictive American maths card game 24game is to try and arrive at the target answer of 24 from each of the following seven groups of numbers. In each calculation, all four digits must be used exactly once each, with + – × ÷ available.

But it is impossible to reach 24 with one of these seven groups:

  •    2    2    2    3
  •    2    2    2    4
  •    2    2    2    5
  •    2    2    2    6
  •    2    2    2    7
  •    2    2    2    8
  •    2    2    2    9

Which one?

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 2nd & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

What is the sum of the multiples of 7?

The Factors Challenge

Which of the following numbers are factors of 314?

4    6    8    10    12    14    16    18    None of them

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

11    22    33    44    55    66    77    88    99    110

#11TimesTable

The Target Challenge

Can you arrive at 314 by inserting 4, 9, 16, 25 and 36 into the gaps below?

  •  (◯+◯)×(◯–◯)–◯ = 314

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 313:

The Main Challenge

Consider the four groups of numbers 3 3 3, 4 4 4, 5 5 5 and 6 6 6.

There are only six target numbers it is possible to make in the range 10-30 when + – × ÷ is available to use.

One of these is 12, which can be made by doing either 3×3+3 or 4+4+4. Can you find the other FIVE target numbers it is possible to make using one or more of these four groups?

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 2nd & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

Which number is the product of two other numbers on the list?

The Factors Challenge

Which of the following numbers are factors of 313?

3     7     9     11     13     17     19     None of them

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which are the only TWO 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 313 by inserting 1, 3, 5, 7 and 9 into the gaps below?

  •  ◯³–(◯–◯)×◯×◯ = 313

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 312:

The Main Challenge

By using the formula (a×b)+c, where a b and c are three unique digits from 1-9, one way of arriving at 24 is (5×3)+9, but can you find the only other way of making 24 when using the above rule.

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 2nd & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

Which three pairs of numbers all have a difference of 47?

The Factors Challenge

Which is the ONLY one of the following that is not a factor of 312?

2     3     4     6     8     9     12     13

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which are the only THREE numbers 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 312 by inserting 2, 3, 4, 6 and 8 into the gaps below?

  •  (◯+◯+◯)×◯×◯ = 312

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 311:

The Main Challenge

Further details of my popular Mathelona number puzzle can be found by clicking this Mathelona link.

Can you make all four lines work out arithmetically by filling the 16 gaps below with digits 0-9? Each digit can only be inserted a maximum of TWICE:

◯  +  ◯   =    9    =   ◯  +  ◯
◯  +  ◯   =    9    =   ◯  –  ◯
◯  +  ◯   =    9    =   ◯  ×  ◯
◯  +  ◯   =    7    =   ◯  ÷  ◯

Were you able to complete this without repeating the same sum when making 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 2nd & 5th rows contain the following fourteen numbers:

6   7   8   16   17   21   28   48   50   55   63   64   81   84

How many factors of 48 are listed?

The Factors Challenge

Which of the following numbers are factors of 311?

3     5     7     9     11     13     None of them

The Mathematically Possible Challenge

Using 47 and 11 once each, with + – × ÷ available, which are the only TWO numbers it 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 311 by inserting 1, 2, 3, 4 and 5 into the gaps below?

  •  (◯³×◯)–(◯⁴×◯×◯) = 311

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 310:

The Main Challenge

Test your knowledge of number combinations by listing the SIX different ways of making 20 when adding together five unique digits from 1 to 9 in this Kakuro-style question.

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 & 3rd rows contain the following fourteen numbers:

2   9   13   14   15   22   25   36   40   42   45   66   72   80

Can you find FIVE sets of three different numbers, all of which have a sum of 100?

The Factors Challenge

Which one of the following numbers is NOT a factor of 310?

1     2     3     5     10     31     62

The Mathematically Possible Challenge

Using 47 and 11 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 310 by inserting 1, 2, 3, 4 and 5 into the gaps below?

  •  (◯³+◯–◯–◯)×◯ = 310

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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