## DAY/DYDD 178: The Main Challenge

Can you arrive at the target answer of 7 by using each of the numbers 0.2, 0.5, 2 and 2.5 exactly once each, and 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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

What is the sum of the factors of 36? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 178, in TWELVE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which SEVEN target numbers from the list below can be made?

6    12    18    24    30    36    42    48    54    60

#6TimesTable The Target Challenge

Can you arrive at 178 by inserting 10, 11, 16 and 20 into the gaps on each line?

•  ◯×◯+◯÷◯ = 178
•  ◯×◯+double(◯–◯) = 178  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 177: The Main Challenge

You must try and make all three lines work out arithmetically by inserting the twelve digits 0 0 1 1 2 3 3 4 5 6 6 and 7 into the gaps:

◯  +  ◯   =    7    =   ◯  –  ◯
◯  +  ◯   =    5    =   ◯  ×  ◯
◯  +  ◯   =    6    =   ◯  ÷  ◯

If you enjoy this, click Mathelona for further details of our unique number puzzles. 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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Which two numbers have a difference of 21? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 177, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which FOUR target 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 177 by inserting 1, 7, 9 and 11 into the gaps on each line?

•  ◯×(◯+◯)+◯ = 177
•  ◯²+(◯–◯)×◯ = 177  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 176: The Main Challenge

You have been given the task of manually numbering a 100-page document from 1 to 100. What is the total of all the individual digits written? 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 1st & 6th rows contain the following fourteen numbers:

2   5   9   12   14   15   18   20   22   33   40   49   56   72

Find three pairs of numbers that each have a sum of 42. The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 176, in TWO different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 36 and 12 once each, with + – × ÷ available, which THREE target 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 176 by inserting 6, 7, 8 and 9 into the gaps on each line?

•  (◯+◯+◯)×◯ = 176
•  ◯²+◯²+◯²–treble◯ = 176  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 175: The Main Challenge

Three people answered the same four multiple choice problems. They had a choice of A, B or C for each question. Their responses are shown here:

• Timmy:    A  B  B  C
• Tammy:   A  C  B  A
• Tommy:   B  B  C  A

Two people answered two questions correctly and one person had them all wrong. Can you work out what the correct answers could be? There is more than one solution! 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

There are four square numbers listed above. Which one has the most factors? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 175, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it 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 175 by inserting 1, 5, 10 and 15 into the gaps on each line?

•  ◯²+(◯×◯×◯) = 175
•  ◯²–(◯×◯×◯) = 175
•  (◯+◯)×◯+double◯ = 175
•  (◯+◯)×◯+treble◯ = 175  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 174: The Main Challenge

• I am a 2-digit number,
• I am a multiple of 7,
• The difference between my two digits is 4.

Which number 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Which number, when 1 is subtracted from it, becomes a square number? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 174, in NINE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which THREE target 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 174 by inserting 9, 10, 16 and 20 into the gaps on each line?

•  (◯+◯)×(◯–◯) = 174
•  ◯×◯+◯–◯ = 174  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 173: The Main Challenge

When allocating each letter of the English alphabet a numerical value as follows; A=1 B=2 C=3 … Z=26, the value of the word SUM, for example, would be 19+21+13 = 53.

What would be the value of our popular number puzzle, 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

Find three pairs of numbers that have a sum that is also on the list. The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 173, in SEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which THREE target numbers is it possible to make from the list below?

1     8     27     64     125

#CubeNumbers The Target Challenge

Can you arrive at 173 by inserting 5, 7, 14 and 15 into the gaps on each line?

•  (◯×◯)+(◯×◯) = 173
•  ◯×(◯+◯)–half◯ = 173  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 172: The Main Challenge

You are playing our Mathematically Possible board game and have rolled the numbers 6, 6 and 6 with your three dice.  Using these once each, with + – × ÷ available, which SIX target numbers from 1-30 is it 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

What is the difference between the sum of the multiples of 7 and the sum of the multiples of 9? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 172, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the SIX target numbers it’s 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 172 by inserting 3, 4, 5 and 8 into the gaps on each line?

•  (◯+◯×◯)×◯ = 172
•  (◯+◯)²+◯²+◯ = 172  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 171: The Main Challenge

You have the same starting number and final answer, both 22.

There are 10 arithmetical steps altogether but the 10th, and final, step is missing. If this final step involves a whole number, what should it be to make the final answer 22?

+2   ÷6   ×4   3   ×2   +4   ÷5   +6   ×2   ?   =   22 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 3rd & 5th rows contain the following fourteen numbers:

6   7   13   16   21   25   36   42   45   50   66   80   81   84

List three sets of three numbers that all have a sum of 100, the numbers in each set must be different. The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 171, in TEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO target numbers it is possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable The Target Challenge

Can you arrive at 171 by inserting 3, 69 and 10 into the gaps on each line?

•  ◯×◯×◯–◯ = 171
•  (◯+◯+◯)×◯ = 171  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 170: The Main Challenge

Study the seven clues and place the numbers 1-9 into the nine positions on this 3-by-3 grid. Each number should appear exactly once:

x              x              x

x              x              x

x              x              x

Clues:

1.  The 8 is directly above the 5,
2.  The 6 is further right than the 7,
3.  The 7 is further right than the 1,
4.  The 1 is lower than the 5,
5.  The 5 is further right than the 9,
6.  The 3 is higher than the 9 and further right than the 2,
7.  The 4 is higher than the 7 and further right than the 8. 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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

What is the difference between the sum of the highest and lowest even numbers and the product of the highest and lowest even numbers? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 170, in ELEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which is the ONLY target number it’s possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable The Target Challenge

Can you arrive at 170 by inserting 9, 10, 20 and 20 into the gaps on each line?

•  ◯+◯×◯–◯ = 170
•  (◯–◯÷◯)×◯ = 170  Click Paul Godding for details of online maths tuition. ## DAY/DYDD 169: The Main Challenge

Three unique digits from 1-9 must be used to arrive at the target number 18 when multiplying two numbers together and adding or subtracting the third unique number, (a×b)±c.

One way of arriving at 18 is (5×4)2.  Find the other FOUR ways it is possible to make 18.

[Note:  (5×4)–2 = 18 and (4×5)2 = 18  counts as just ONE way.] 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 & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Which number above 20 becomes a multiple of 11 when 20 is subtracted from it? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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 169, in EIGHT different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only FOUR numbers it’s 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 169 by inserting 1, 3, 13 and 15 into the gaps on each line?

•  ◯×(◯+◯–◯) = 169
•  (◯–◯)²+(◯÷◯)² = 169   