DAY 295:

The Main Challenge

. . . is from Volume 1 of our Mathelona pocket book. You have a limited amount of numbers to work with, so can you make all three lines work out arithmetically by filling the 12 gaps with these numbers?

1      2      2      2      3      4      4      4      8      8      8      8

◯  +  ◯   =     5     =   ◯  –  ◯
◯  +  ◯   =    16    =   ◯  ×  ◯
◯  +  ◯   =     4     =   ◯  ÷  ◯

Full details of our popular number puzzle can be found by clicking 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 2nd & 3rd rows contain the following fourteen numbers:

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

There are two numbers on the list that are consecutive. What is their sum?

The Factors Challenge

Which of the following numbers are factors of 295?

3     5     7     9     11     13     15

The Mathematically Possible Challenge

Using 810 and 12 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

80    81    82    83    84    85    86    87    88    89

#NumbersIn80s

The Target Challenge

Can you arrive at 295 by inserting 3, 3, 4, 5 and 6 into the gaps below?

  •  (◯³÷◯–◯²+◯)×◯ = 295

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 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 individual 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, five of which are posted each day, and the majority are our very own creations.

There are seven categories you will see posted throughout the year:

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 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 educational purposes in schools, or even at home and 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, 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 294:

The Main Challenge

This is a Banana & Clock Puzzle which caused quite a stir and promoted lots of discussion on twitter:

What do you think the answer on the final line is?

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 highest and lowest multiples of 6?

The Factors Challenge

Which FOUR from the following list of numbers are factors of 294?

2     3     4     5     6     7     8     9

The Mathematically Possible Challenge

Using 810 and 12 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

60    61    62    63    64    65    66    67    68    69

#NumbersIn60s

The Target Challenge

Can you arrive at 294 in two different ways when inserting 3, 4, 5, 6 and 7 into the gaps below?

  •  ◯×◯×(◯×◯–◯) = 294

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 293:

The Main Challenge

Here is a FlagMath-style puzzle derived from our series of card games.

Each of the eleven letters, A-K, in the two sections below contains a percentage calculation. Which is the only letter to have the SAME answer in BOTH sections?

  • Section 1

F: 40% of 60    A: 25% of 20    G: 50% of 30    B: 60% of 35    D: 20% of 40    J: 30% of 5   K: 16% of 50    C: 70% of 30    H: 15% of 60    E: 10% of 100    I: 5% of 80

  • Section 2

H: 1% of 500    D: 80% of 10    K: 2% of 200    G: 30% of 80    J: 20% of 50    F: 10% of 40   C: 25% of 60    I: 70% of 20    A: 15% of 200    E: 5% of 140    B: 8% of 300

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

When finding the highest multiple of 7 on the list, what is double this number?

The Factors Challenge

Which of the following numbers are factors of 293?

3     5     7     9     11     13     None of them

The Mathematically Possible Challenge

Using 810 and 12 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 293 in two different ways when inserting 4, 9, 16, 25 and 36 into the gaps below?

  •  ◯²+◯+√◯+√(◯×◯) = 293

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 292:

The Main Challenge

Following on from DAY 240, here’s another one of the unique Keith Number challenges made famous by Mike Keith and similar to the Fibonacci sequence. If you like playing around with numbers, you’ll love having a go at this fun concept.

The 1st 2-digit Keith Number14, is worked out by following a pattern:

  •    1   4   5   9   14

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

The 2nd 2-digit Keith Number19, is worked out in a similar way:

  •    1   9   10   19

1+9=10; 9+10=19 (the total again arrives back to the original number).

By following this pattern, the 3rd and 4th 2-digit Keith Numbers are 28 and 47:

  •    2   8   10   18   28
  •    4   7   11   18   29   47

Can you continue this process and locate the only other two Keith Numbers below 100?

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 square numbers?

The Factors Challenge

Which of the following numbers are factors of 292?

6    8    10    12    14    16    18    None of them

The Mathematically Possible Challenge

Using 810 and 12 once each, with + – × ÷ available, which are the only TWO numbers it is 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 292 by inserting 2, 3, 4, 5 and 6 into the gaps below?

  •  ◯×(◯³×◯²+(◯–◯)²) = 292

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 291:

The Main Challenge

Read the following facts to work out my identity:

  • I am a 2-digit number
  • my two digits have a difference of four
  • add 13 to me and I become 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 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 highest and lowest multiples of 5?

The Factors Challenge

Which of the following numbers are factors of 291?

3     5     7     9     11     13     None of them

The Mathematically Possible Challenge

Using 810 and 12 once each, with + – × ÷ available, which is the ONLY number 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 291 by inserting 2, 3, 3, 5 and 6 into the gaps below?

  •  ◯×(◯²×(◯+◯)–◯) = 291

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 290:

The Main Challenge

When using the numbers 3, 3 and 4 once each, with – × ÷ available, list the TEN target numbers from 1-30 that are mathematically 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 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 listed are the product of two different pairs of numbers on the list?

The Factors Challenge

Which THREE prime numbers listed below are factors of 290?

2    3    5    7    11    13    17    19    23    29

The Mathematically Possible Challenge

Using 810 and 12 once each, with + – × ÷ available, which are the THREE numbers it is 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 290 in two different ways when inserting 10, 30, 50, 70 and 90 into the gaps below?

  •  (◯×◯÷◯)+◯ = 290

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 289:

The Main Challenge

What is the biggest number you can make when using the four digits 1 2 3 4 and following these rules:

  • you can use brackets and – × ÷ as often as you like,
  • you cannot use any number more than once,
  • you must use all four numbers exactly once each,
  • you cannot use powers/indices,
  • you cannot put numbers together (using 1, 2 and 3 to make 123, for example).

Good luck and enjoy!

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

Find three different numbers that have a sum of 100.

The Factors Challenge

Which is the ONLY number from the following list that is a factor of 289?

3    5    7    9    11    13    15    17    19

The Mathematically Possible Challenge

Using 810 and 12 once each, with + – × ÷ available, which are the FOUR numbers it is 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 289 by inserting 2, 3, 4, 6 and 7 into the gaps below?

  •  (◯×◯–◯)²+◯²◯² = 289

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 288:

The Main Challenge

Try and arrive at the target answer of 7 by using each of the numbers 0.2, 0.2, 5 and 6 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

What is the product of the two prime numbers listed?

The Factors Challenge

Which is the ONLY number from the following list that is not a factor of 288?

2    3    4    6    8    9    12    14    16    18

The Mathematically Possible Challenge

Using 810 and 12 once each, with + – × ÷ available, which are the FOUR 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 288 by inserting 2, 3, 4, 6 and 8 into the gaps below?

  •  (◯+◯+◯)××◯ = 288

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 287:

The Main Challenge

When allocating each letter of the English alphabet a numerical value as follows, A=1 B=2 C=3 . . . Z=26, calculate your answer when adding up the values of the individual letters of:

MATHEMATICALLY POSSIBLE

Take a browse at our popular strategy board game by clicking Mathematically Possible.

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 pairs of numbers all have a difference of 17?

The Factors Challenge

Which is the ONLY number from the following list that is a factor of 287?

3     5     7     9     11     13     15     17

The Mathematically Possible Challenge

Using 27 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

80    81    82    83    84    85    86    87    88    89

#NumbersIn80s

The Target Challenge

Can you arrive at 287 by inserting 2, 3, 4, 5 and 6 into the gaps below?

  •  ◯²×◯²×◯+◯ = 287

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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