DAY 203:

The Main Challenge

Starting with the number 7, complete the following sixteen arithmetic steps:

  • multiply by ten
  • 40 percent of this
  • double it
  • multiply the digits together
  • increase by 20 percent
  • divide by three
  • increase by 50 percent
  • one-third of this
  • double it
  • square it
  • five-sixths of this
  • decrease by 10 percent
  • divide by three
  • add thirty-nine
  • increase by 20 percent
  • seven-ninths of this

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 1st & 3rd rows of the playing board contain the following fourteen numbers:

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

What is the difference between the sum of the odd numbers and sum of the even 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 xxxxxx different ways to make 203 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 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 203 by inserting 347 and 8 into the gaps on each line?

  •  (◯×◯–◯)×◯ = 203
  •  (◯+◯)²–◯²–double◯ = 203
  •  ◯³–◯×(◯³+◯) = 203

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 202:

The Main Challenge

If you added together the first seven odd numbers that do not contain a 3, 5 or 7 as part of their number or are not multiples of 3, 5 or 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 2 up to 84.

The 1st & 3rd rows of the playing board contain the following fourteen numbers:

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

What is the average of the three consecutive numbers 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 THIRTEEN different ways to make 202 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 and 11 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 202 by inserting 7813 and 14 into the gaps on each line?

  •  ◯×◯+◯×◯ = 202
  •  ◯²+(◯–◯)²–double◯ = 202

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 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, you can type into the address bar:

  •  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 are 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 – 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 201:

The Main Challenge

When playing Mathematically Possible, players analyse which target numbers can (or cannot) be made from the three numbers rolled on their dice, but this particular challenge is slightly different as you are only allowed to add and subtract (+ and –) when calculating.

Use the numbers 3, 6 and 10 once each to find the only FOUR target numbers from 1-30 that are mathematically possible to achieve.

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 of the playing board contain the following fourteen numbers:

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

What is the sum of the multiples of 7 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 TEN different ways to make 201 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 and 11 once each, with + – × ÷ available, which are the only 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 201 by inserting 358 and 9 into the gaps on each line?

  •  (◯×◯–◯)×◯ = 201
  •  (◯+◯)²+◯–◯ = 201

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 200:

Today’s Challenge

Playing the superb American maths card game, 24game®, can be frustrating but very addictive when testing your arithmetical skills.

When using four numbers just once each, with + – × ÷ available, it is only possible to make 24 with one of the seven groups of numbers below:

  •      1    1    7    6
  •      1    1    7    7
  •      1    1    7    8
  •      1    1    7    9
  •      1    1    7   10
  •      1    1    7   11
  •      1    1    7   12

. . . but 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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

Which is the only cube number 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 FOUR different ways to make 200 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 and 11 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 200 by inserting 101525 and 30 into the gaps on each line?

  •  ◯×◯–◯×◯ = 200
  •  (◯–◯÷◯)×◯ = 200

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 199:

The Main Challenge

Follow the rules and only one number will remain.

Eliminate the following in the range 1-50: 

  •  multiples of 3
  •  square numbers
  •  prime numbers
  •  even numbers

Which number from 1-50 will be the last one standing?

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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

Which number, when 20 is added to it, becomes a square number?

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 199 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 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 199 by inserting 111214 and 20 into the gaps on each line?

  •  ◯×◯+◯+◯ = 199
  •  ◯²+◯+◯–◯ = 199

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 198:

The Main Challenge

What is the LOWEST whole number that satisfies all three criteria below?

  • it is the sum of five consecutive whole numbers,
  • it is the sum of two consecutive odd numbers,
  • it is the sum of three consecutive even numbers.

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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

List five different numbers that have a sum of 70.

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 ELEVEN different ways to make 198 when using Lagrange’s Theorem. How many can you find?

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 57 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is 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 198 by inserting 467 and 9 into the gaps on each line?

  •  (◯×◯–◯)×◯ = 198
  •  (treble◯+◯×√◯)×◯ = 198

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 197:

The Main Challenge

There is just one set of three consecutive numbers in ascending order whose sum is less than 50 and follow this sequence:

  •  prime number – cube number – square number

What is the sum of these three numbers?

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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

What is the sum of the multiples 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).

Show how you can make 197, in SEVEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 34 and 12 once each, with + – × ÷ available, which FOUR numbers is it 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 197 by inserting 1411 and 14 into the gaps on each line?

  •  ◯×(◯+◯)–◯ = 197
  •  (◯+◯)²–(◯×double◯) = 197

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 196:

The Main Challenge

Here’s a 10-step number trail involving the four arithmetical operations, some 3-digit numbers, plus fractions and percentages.

Start with the number 2, then:

  • add three hundred and eighty
  • 292
  • +106
  • 50%
  • 1/2 of this
  • multiply by nine
  • 1/3 of this
  • 7
  • divide by seven
  • +7

What’s your 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 6th & 7th rows of the playing board contain the following fourteen numbers:

4   5   11   12   18   20   24   27   30   33   49   56   70   77

What is half of the highest even number?

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).

Show how you can make 196, in TEN different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 34 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45    55    66

#TriangularNumbers

The Target Challenge

Can you arrive at 196 by inserting 568 and 9 into the gaps on each line?

  •  (◯+◯)×(◯+◯) = 196
  •  (◯+◯)²+(◯×half◯) = 196
  •  (◯+◯)²–(²+half◯) = 196
  •  ◯³+◯–(◯+double◯) = 196
  •  ◯³+◯–(◯²+√◯) = 196

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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DAY 195:

The Main Challenge

In this Kakuro-style question, can you list ONLY way possible to make 16 when adding together five unique digits from 1-9?

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 4th & 5th rows of the playing board contain the following fourteen numbers:

3   6   7   10   16   21   32   35   44   50   54   60   81   84

How many pairs of numbers differ by exactly 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).

Show how you can make 195, in NINE different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Based on our best-selling arithmetic board game.

Using 34 and 12 once each, with + – × ÷ available, which TWO numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers

The Target Challenge

Can you arrive at 195 by inserting 5, 8, 13 and 18 into the gaps on each line?

  •  (◯+◯+◯)×◯ = 195
  •  (◯+◯–◯)×◯ = 195

Answers can be found here.

Click Paul Godding for details of online maths tuition.

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