DAY/DYDD 17:

The Main Challenge

Find the answer to this large number trail which involves fourteen arithmetical steps and includes fraction and percentage calculations.

Start with the number 11, then:

  • double it
  • 50% of this
  • +50
  • subtract thirty-five
  • ÷2
  • +37
  • 3/5 of this
  • +70
  • 2%
  • 1/2 of this
  • +311
  • subtract twenty
  • add ten
  • ÷7

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 up to 84.

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

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

What is the difference between the highest multiples of 5 and 6?

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 only TWO ways of making 17 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 56 and 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 17 by inserting 2, 5, 6 and 6 into the gaps on each line?

  •  ◯²–√(◯×◯)–◯ = 17
  •  ◯²×◯÷◯+◯ = 17
  •  (◯÷◯+◯)×◯ = 17

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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WELCOME/CROESO

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, 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, 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.

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/DYDD 16:

The Main Challenge

What is the sum of the 50 integers (or whole numbers) from 1 through to 50 inclusive?

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 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 factors of 24 listed above?

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 only TWO ways of making 16 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number 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 16 by inserting 3, 4, 6 and 8 into the gaps on each line?

  •  ◯×◯×◯÷◯ = 16
  •  ◯²–◯×(◯–◯) = 16
  •  ÷◯׳√◯×◯ = 16

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 15:

The Main Challenge

Your task is to multiply two numbers together and then subtract a third number to achieve the target answer of 7. The three numbers used in each calculation must all be unique digits from 1-9.

For example, one such way of making 7 is (4×3)5. Can you find SIX other ways to make 7?

[Note:  (4×3)5 = 7  and  (3×4)5 = 7  counts as 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 contain the following fourteen numbers:

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

What is the difference between the total of the prime numbers and the sum of the multiples of 10?

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 of making 15 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number 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 15 by inserting 2, 3, 5 and 6 into the gaps on each line?

  •  ◯×◯+◯◯ = 15
  •  ◯÷ײ×◯ = 15
  •  ◯²–(◯+◯)× = 15

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 14:

The Main Challenge

Insert the 12 numbers 1 1 2 2 2 3 5 5 6 7 8 and 8 so that all three lines work out arithmetically:

◯  +  ◯   =     6     =   ◯  –  ◯
◯  +  ◯   =    14    =   ◯  ×  ◯
◯  +  ◯    =    5     =   ◯  ÷  ◯

If you enjoyed trying this puzzle, visit our Mathelona page 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 contain the following fourteen numbers:

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

What is the difference between the highest and lowest 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 is only ONE way of making 14 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which is the ONLY number 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 14 by inserting 2, 4, 5 and 5 into the gaps on each line?

  •  ◯+◯+◯+√◯ = 14
  •  ◯²–(◯+◯+◯) = 14
  •  (◯+÷◯)× = 14

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 13:

The Main Challenge

Starting from 2, list the first seven even numbers that are NOT multiples of 3, 5 or 7. What is the 7th number in your list?

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 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 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 TWO ways to make 13 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which THREE 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 13 by inserting 1, 2, 3 and 4 into the gaps on each line?

  •  ◯×◯+◯–◯ = 13
  •  ◯×(◯+◯)+ = 13
  •  (◯²+²+◯)÷◯ = 13

Answers can be found here.

Click Paul Godding for details of online maths tuition. 

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DAY/DYDD 12:

The Main Challenge

Add together the 7th prime number, the 7th square number, the 7th 2-digit number and the 7th whole number that contains a 7. What is your answer?

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 contain the following fourteen numbers:

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

Which two numbers listed have a sum of 101?

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 TWO ways to make 12 when using Lagrange’s Theorem. Can you find both?

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

40    41    42    43    44    45    46    47    49    49

#NumbersIn40s

The Target Challenge

Can you arrive at 12 by inserting 2, 3, 4 and 6 into the gaps on each line?

  •  (◯–◯)×◯×◯ = 12
  •  ◯×◯(◯+◯) = 12
  •  ◯÷◯×(◯+◯) = 12
  •  ◯²–◯×◯÷◯ = 12
  •  (◯²+◯³)×◯÷◯ = 12

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 11:

The Main Challenge

Today’s task is to arrive at the target number of 7 by using the four numbers 7, 7, 7 and 7 once each. All four arithmetic operations + – × ÷ are available. Can you make 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 5th & 6th rows contain the following fourteen numbers:

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

From this list, what is the sum of the square 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 is only ONE way to make 11 when using Lagrange’s Theorem. Can you find it?

The Mathematically Possible Challenge

Using 45 and 10 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 11 by inserting 2, 3, 4 and 5 into the gaps on each line?

  •  ◯×◯+◯–◯ = 11
  •  ◯÷◯×◯+◯ = 11
  •  ◯²(◯×(◯+◯)) = 11

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 10:

The Main Challenge

Using seven 7’s (7 7 7 7 7 7 and 7) once each, with + – × ÷ available, it is possible to make various target answers, such as 7 as shown here:

  • 7+7+7+7777 = 7,  or perhaps
  • 7×(7÷7)×(7÷7)×(7÷7) = 7

In a similar way, show how to make the target answers 1, 2 and 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 3rd & 4th rows contain the following fourteen numbers:

3   10   13   25   32   35   36   42   44   45   54   60   66   80

What is the sum of the multiples of 4?

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of 10 with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 10?

  •   1   1   6
  •   1   2   6
  •   1   5   5
  •   2   2   3
  •   2   4   5
  •   3   5   5
  •   4   5   6

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 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 10 by inserting 2, 2, 3 and 5 into the gaps on each line?

  •  (◯–◯)×◯×◯ = 10
  •  (◯–◯÷◯)×◯ = 10
  •  (◯²–◯–◯)÷◯ = 10
  •  ◯÷(◯–◯÷◯) = 10

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY/DYDD 9:

The Main Challenge

. . . is from the excellent card game, 24game. Using the numbers 2, 4, 6 and 8 once each, and with all four operations + – × ÷ available, show how you can reach the target number of 24.

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

3   10   13   25   32   35   36   42   44   45   54   60   66   80

From the list, find the THREE pairs of numbers that have a sum of 57.

The Roll3Dice Challenge

From the seven groups of numbers below, it is possible to make today’s target number of with six of the groups when each number in the group is used once and + – × ÷ is available.

But, which is the impossible group below that CANNOT make 9?

  •   1   2   3
  •   1   3   4
  •   2   2   5
  •   3   3   4
  •   3   5   6
  •   4   5   5
  •   4   6   6

Visit Roll3Dice.com for full details of our family-related maths initiative.

The Mathematically Possible Challenge

Using 45 and 10 once each, with + – × ÷ available, which is the ONLY number 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 9 by inserting 3, 4, 5 and 6 into the gaps on each line?

  •  ◯×◯–(◯+) = 9
  •  ◯+×(–◯) = 9
  •  ◯²–◯×(÷◯)² = 9
  •  ◯+(◯+◯)÷◯ = 9

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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