DAY 229:

The Main Challenge

There are five different 24game® challenges below.

For each group of four numbers, your task is to arrive at the target answer of 24 by using each of the four digits exactly once, with + – × ÷ available:

  •   1    2    3    4
  •   2    3    4    5
  •   3    4    5    6
  •   4    5    6    7
  •   5    6    7    8

All five challenges are possible, can you do it?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 1st & 7th rows of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the total when adding together all the odd numbers?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are SEVEN different ways to make 229 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 24 and once each, with + – × ÷ available, which FIVE 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 229 by inserting 2, 3, 4, 5 and 7 into the gaps below?

  •  ◯²×◯+◯²×◯+◯ = 229

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. These are 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 help 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, in the address bar you can type:

  •  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 puzzlers must arrive at that particular day’s target number using his 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 answers? Requires perseverance!

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 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, 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 228:

The Main Challenge

You have been given a starting number as well as an end answer. There are seven arithmetical steps in all, but the middle step is missing!

Start with the number 7, then:

2    ×4    +1    ?    ×5    ÷3    +2    =    7

The missing step involves a single-digit whole number.  Work out this missing step so the final answer will also be 7.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 1st & 7th rows of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which four different numbers above have a sum of 100?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are NINE different ways to make 228 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 24 and once each, with + – × ÷ available, which FOUR 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 228 by inserting 34, 5 and 6 into the gaps on each line?

  •  ◯×(◯²+◯²–◯) = 228
  •  ◯×(◯²×◯+double◯) = 228

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 227:

The Main Challenge

Firstly, allocate each letter of the English alphabet a numerical value as follows: A=1, B=2, C=3 . . . Z=26.  When the values of the individual letters are added together, calculate the total value of our popular maths card game, FlagMath.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 1st & 7th rows of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

What is the sum of the square numbers present on the list?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are SEVEN different ways to make 227 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 24 and 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 227 by inserting 38, 10 and 15 into the gaps on each line?

  •  (◯+◯)×◯–◯ = 227
  •  (◯+◯)×◯+◯³ = 227 

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 226:

The Main Challenge

Your task is to arrive at the target number of 47 by using all five numbers 1, 2, 3, 4 and 5 exactly once each. Can you arrive at 47 in two different ways?

Remember, you have – × ÷ available to use in both calculations.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 1st & 7th rows of the playing board contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

From the list, how many multiples of 8 are there?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are TWELVE different ways to make 226 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 24 and once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

The Target Challenge

Can you arrive at 226 by inserting 45, 6 and 7 into the gaps on each line?

  •  ◯×◯×◯+◯² = 226
  •  ◯²×double◯+double(◯+◯) = 226

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 225:

The Main Challenge

Each of the five numbers below is the product of two prime numbers:

15     35     77     143     323

Which is the odd one out, and why?

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the sum of the multiples of 7?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are FOURTEEN different ways to make 225 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

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

15    30    45    60    75    90    105    120    135    150

#15TimesTable

The Target Challenge

Can you arrive at 225 by inserting 345 and 9 into the gaps on each line?

  •  (◯–◯)×◯×◯² = 225   (2 ways!)
  •  (◯+◯+◯–◯)² = 225

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 224:

The Main Challenge

Today’s task is you multiply two numbers together, then either add or subtract the third number to achieve the target answer of 37.

Using the formula (a×b)±c, where a, b and c are three unique digits from 1-9, one way of achieving 37 is (7×5)+2; can you find the other SEVEN ways?

[Note: (7×5)+2 = 37 and  (5×7)+2 = 37 counts as just ONE way.]

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

From the list, which three different numbers have a sum of 100?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There is only ONE way to make 224 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

13    26    39    52    65    78    91    104    117    130

#13TimesTable

The Target Challenge

Can you arrive at 224 by inserting 127 and 7 into the gaps on each line?

  •  ◯×◯²×(◯+◯) = 224
  •  ◯⁵×◯³×◯²÷◯ = 224

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 223:

The Main Challenge

Try the following MATHELONA challenge, just like the ones in my number puzzle pocket book.  Further details can be found by clicking on MATHELONA.

Your task is to make all three lines work out arithmetically by replacing the 12 ◯’s below with  0  0  1  1  2  2  3  3  4  4  6  6.  Can you do it?

◯  +  ◯   =    4    =   ◯  –  ◯
◯  +  ◯   =    6    =   ◯  ×  ◯
◯  +  ◯   =    3    =   ◯  ÷  ◯

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the answer when the larger multiple of 10 is divided by the smaller one?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are NINE different ways to make 223 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

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

1    3    5    7    9    11    13    15    17    19

#OddNumbers

The Target Challenge

Can you arrive at 223 by inserting 378 and 20 into the gaps on each line?

  •  ◯²×◯+◯×◯ = 223
  •  (◯⁵–◯)÷(◯–◯) = 223

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 222:

The Main Challenge

You’ve rolled the numbers 1, 3 and 3 with your three dice.  Using these once each, with + – × ÷ available, find the TWO target numbers from 1-10 that it is NOT possible to make.

Visit Roll3Dice.com and the hashtag #Roll3Dice for further details.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the sum of the multiples of 5 on the list?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are TEN different ways to make 222 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

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

2    4    6    8    10    12    14    16    18    20

#EvenNumbers

The Target Challenge

Can you arrive at 222 by inserting 356 and 8 into the gaps on each line?

  •  (◯×◯–◯)×◯ = 222
  •  ◯³+◯+◯–◯ = 222

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 221:

The Main Challenge

Group the following numbers into three lots of three so the products of each of the triples are the same. What is this product?

3     4     5     6     7     8     28     30     35

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid containing 49 different numbers, ranging from up to 84.

The 5th & 6th rows of the playing board contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

From the list, which pair of numbers have a sum of 77?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive 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).

There are NINE different ways to make 221 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 46 and once each, with + – × ÷ available, which are the only THREE numbers 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 221 by inserting 567 and 10 into the gaps on each line?

  •  (◯+◯)²–◯×◯ = 221
  •  (◯+◯+1)×(◯+◯+1) = 221

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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