The World's #1 Daily Number Puzzle Website

The Main Challenge

Start with the number 50, then:

+27  –42   divide by 5  ×4   +50%   two-thirds of this   ÷7   =    ?

What is your final answer to this 7-step number trail?

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the difference between the highest odd number and lowest multiple of 11?

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 FIVE ways of making 143 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the SIX 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 143 by inserting 3, 4, 7 and 10 into the gaps on each line?

•  (◯+◯)×(◯+◯) = 143
•  ◯³–◯²×double(◯–◯) = 143

Answers can be found here.

Click Paul Godding for details of online maths tuition.

A warm Welsh welcome 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, Bing, Yahoo, Baidu, DuckDuckGo, Excite 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, nearly 2,000 on this website, the majority of which are our very own creations.

They have been placed into 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 can be manipulated to arrive at the target number, but your task is to find the impossible group of three numbers!

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.

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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

The Main Challenge

From the numbers 1-20, eliminate all:

• square numbers
• prime numbers
• triangular numbers
• multiples of 6

Add together the numbers that remain; what is your total?

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

From this list, what is the sum of the multiples of 8?

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 FIVE ways of making 142 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only TWO 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 142 by inserting 4, 9, 10 and 13 into the gaps on each line?

•  ◯×◯+◯×◯ = 142
•  ◯×◯+◯×√◯ = 142

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

One of our easier Mathelona-style challenges, still utilising the four arithmetic operations.  Place the eight digits 1 2 2 3 4 4 5 and 6 into the gaps so both lines work out:

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

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

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 & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

What is the difference between the two 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 SIX ways of making 141 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using the three digits 2, 6 and 9 once each, with + – × ÷ available, which are the only THREE 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 141 by inserting 3, 5, 7 and 12 into the gaps on each line?

•  ◯×(◯+◯)–◯ = 141
•  (◯×◯+◯)×◯ = 141
•  ◯³+◯+◯–◯ = 141

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Group the following numbers into three groups of three so that the sum of each of the triples are the same. What is this sum?

11    25    35    43    51    63    73    85    91

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 5th & 7th rows of the playing board contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

How many square numbers are listed?

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 FIVE ways of making 140 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 140 by inserting 2, 6, 8 and 10 into the gaps on each line?

•  ◯²+◯²+◯÷◯ = 140
•  (◯+◯)²–(◯–◯)² = 140
•  ◯³+◯²–◯×◯ = 140

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

There are two sections below, both containing ten letters, A-J.  Each letter is linked to a division calculation:

• Section 1

D:9÷3  H:8÷2  B:12÷3  I:8÷4  A:4÷2  E:24÷6  G:15÷5  C:20÷4  F:25÷5  J:7÷7

• Section 2

I:6÷2  G:6÷3  D:10÷2  E:12÷4  J:14÷7  B:20÷5  A:18÷6  C:10÷5  F:16÷4  H:15÷3

Which is the only letter to contain 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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

How many pairs of numbers from the list have a sum of 88?

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 SIX ways of making 139 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 139 by inserting 3, 7, 9 and 11 into the gaps on each line?

•  ◯×(◯+◯)+◯ = 139
•  ◯²+◯×◯–◯² = 139

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

The two sections below both contain ten letters, A-J; each of which has a multiplication calculation assigned to it:

• Section 1

C:10×2  J:4×3  F:8×5  D:3×3  I:3×2  G:7×4  B:5×4  H:9×4  E:10×3  A:6×4

• Section 2

B:12×2  D:6×1  G:8×3  J:5×2  E:6×5  I:6×6  H:8×6  A:9×2  F:7×2  C:6×3

Which is the only letter that contains 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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

Find three different numbers that 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 TEN ways of making 138 when using Lagrange’s Theorem. Can you find them all?

Can you arrive at 138 by inserting 2, 6, 10 and 15 into the gaps on each line?

•  ◯×◯–◯×◯ = 138
•  (◯+◯–◯)×◯ = 138
•  ◯²+double◯+◯+◯ = 138

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

It is possible to use seven 5’s (5 5 5 5 5 5 and 5) once each, with the four operations + – × ÷, to make all the target numbers from 1 to 5.

For instance, to arrive at the target numbers 1 and 2, you can do:

• [(5+5)÷5 – 5÷5] × 5÷5 = 1
• [(5+5)÷5 – 5÷5] + 5÷5 = 2

Your task is to show how to arrive at the other target numbers 3, 4 and 5.

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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

What is the product of the two prime numbers listed?

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 SIX ways of making 137 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 137 by inserting 4, 5, 6 and 8 into the gaps on each line?

•  ◯³+◯²+◯×◯ = 137
•  ◯³+◯×◯÷◯ = 137

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Can you arrive at the target number 55 by using the five numbers 1, 2, 3, 4 and 5 exactly once each, and with + – ×  ÷ available?

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 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

What is the sum of the factors of 42?

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 FOUR ways of making 136 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 136 by inserting 4, 6, 7 and 8 into the gaps on each line?

•  (◯×◯–◯)×◯ = 136
•  (◯+◯+◯)×◯ = 136

Answers can be found here.

Click Paul Godding for details of online maths tuition.

The Main Challenge

Here’s a number trail involving 16 arithmetical steps.  Start with the number 2, then:

•  +33
•  divide by seven
•  ×3
•  add ten percent
•  double this
•  add three
•  find the square root of this
•  +7
•  1/2 of this
•  add nineteen point five
•  subtract two
•  ÷6
•  +15
•  ×5
•  –93
•  ÷2

What is your final answer?

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 & 6th rows contain the following fourteen numbers:

5   12   13   18   20   25   33   36   42   45   49   56   66   80

Which two numbers, when doubled, are also 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 ways of making 135 when using Lagrange’s Theorem. Can you find them?

Can you arrive at 135 by inserting 4, 5, 9 and 12 into the gaps on each line?

•  ◯²–◯×(◯–◯) = 135
•  ◯×◯×◯÷◯ = 135
•  (◯+◯)²+half(◯×◯) = 135

Answers can be found here.

Click Paul Godding for details of online maths tuition.