## DAY/DYDD/GIORNO/NAP 168: T he Main Challenge

The two sections below both contain eight letters, A-H. Each letter has an addition calculation attached, all involving 2-digit numbers.

Which is the only letter that has exactly the same answer in both sections?

• Section 1

D:68+18   B:51+14   E:47+31   H:62+32   A:44+29   G:59+25   C:36+23   F:38+26

• Section 2

E:64+28   A:31+27   F:34+22   B:43+19   G:48+36   C:54+16   D:48+21   H:50+38 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 three different numbers have a total which is also present 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 168, in FOUR different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 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 168 by inserting 2, 4, 6 and 9 into the gaps on each line?

•  (◯–◯)×◯×◯ = 168
•  ◯³×◯–◯²×◯ = 168  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 167: The Main Challenge

Find the sum of all the numbers between 5 and 25 that are divisible by 3, 4 or 7. 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, when 4 is subtracted from it, becomes a multiple of 15? 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 167, in FIVE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO numbers it’s 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 167 by inserting 8, 9, 10 and 15 into the gaps on each line?

•  ◯×◯+◯+◯ = 167
•  ³√◯×◯²+◯–◯ = 167  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 166: The Main Challenge

This number trail has seven arithmetical steps.

√    add nineteen    50% of this    2    +26    subtract nine    ÷7    =   ? 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 sum of the factors of 24? 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 166, in NINE different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only THREE numbers 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 166 by inserting 4, 7, 14 and 17 into the gaps on each line?

•  (◯×◯)+(◯×◯) = 166
•  (◯+◯)²+◯+double◯ = 166
•  ◯×(◯+◯)–(◯+50%) = 166  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 165: The Main Challenge

Which THREE different prime numbers have a sum of 40? 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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

What is the sum of the factors of 120? 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 165, 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 numbers it’s 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 165 by inserting 5, 10, 15 and 20 into the gaps on each line?

•  (◯+◯)×◯+◯ = 165
•  (◯+◯)×◯–◯ = 165  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 164: The Main Challenge

You have 12 balls and each ball is numbered differently from 1 to 12.  They are randomly placed into two bags so each bag contains the six numbered balls shown below:

• Red bag:   2 3 4 6 9 11
• Blue bag:  1 5 7 8 10 12

You then move a ball from the red bag to the blue bag.  The total of the seven balls in the blue bag is now double the total of the five balls left in the red bag.

Which ball did you move from the red bag to the blue bag? 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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

How many pairs of numbers have a difference of 12? 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 164, in SIX different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which are the only FOUR numbers it’s possible to make from the list below?

2    3    5    7    11    13    17    19    23    29 The Target Challenge

Can you arrive at 164 by inserting 467 and 8 into the gaps on each line?

•  (◯×◯–◯)× = 164
•  ◯²×◯–quarter(³) = 164  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 163: The Main Challenge

Fill the 15 gaps below with the numbers 1-15, once each, so all five lines work out:

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

The concept behind this challenge is similar to my Mathelona number puzzles, so please feel free to click the link for details of my popular pocket book of challenges. 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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which 2-digit number, when 4 is subtracted from it, becomes a multiple 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 163, in SEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which are the only FOUR numbers it’s 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 163 by inserting 579 and 20 into the gaps on each line?

•  ◯×+◯× = 163
•  ◯×+◯+double = 163  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 162: The Main Challenge

Here’s a mini-Mathelona challenge where you must place the eight digits 0, 1, 1, 2, 2, 2, 3 and 4 into the eight gaps so both lines work out arithmetically:

◯  +  ◯   =    4    =   ◯  ×  ◯
◯  –  ◯   =    2    =   ◯  ÷  ◯

Click Mathelona for details of our pocket book challenges. 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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which two numbers, when each is divided by 6, also appear 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 (4+1+1+1).

Show how you can make 162, in THIRTEEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 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 162 by inserting 239 and 12 into the gaps on each line?

•  ◯××(◯–◯) = 162
•  ◯³×(×◯–◯) = 162  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 161: The Main Challenge

Three DIFFERENT digits from 1-9 must be used in a particular way to arrive at a specified target number. The rule is to multiply two numbers together, then either add or subtract the third number, so you arrive at today’s target number of 30.

As an example, one such way of making 30 is (8×3)+6. Can you find the other FOUR ways of making 30?

[Note:  (8×3)+6 = 30  and  (3×8)+6 = 30  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 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which THREE numbers, when 31 is added to each, all become square 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 (4+1+1+1).

Show how you can make 161, in SEVEN different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which SIX numbers is it 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 161 by inserting 3810 and 15 into the gaps on each line?

•  ◯×◯++ = 161
•  (◯+◯)×(◯–◯) = 161  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 160: The Main Challenge

•  I am a 2-digit number,
•  My 1st digit is bigger than my 2nd digit,
•  I am less than 50,
•  I am an odd number,
•  I am not a prime number.

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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which of the multiples of 10 listed above has more 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 (4+1+1+1).

Show how you can make 160, in TWO different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which is the ONLY number it’s 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 160 by inserting 5810 and 12 into the gaps on each line?

•  ◯×◯+◯×◯ = 160
•  ◯²+×÷ = 160
•  ◯××(◯)² = 160  Click Paul Godding for details of online maths tuition. ## DAY/DYDD/GIORNO/NAP 159: The Main Challenge

Can you make all three lines work out arithmetically by placing the numbers 1, 2, 3, 4, 5, 6, 10, 11 and 12 into the nine gaps below?

◯   +   ◯   =   ◯
◯   +   ◯   =   ◯
◯   +   ◯   =   ◯

If you enjoy this type of number puzzle, click Mathelona which will give you full information about our pocket book challenges. 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 & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which number, when 10 is added to it, becomes a multiple of 7? 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 (4+1+1+1).

Show how you can make 159, in SIX different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 once each, with + – × ÷ available, which is the ONLY number it’s 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 159 by inserting 146 and 10 into the gaps on each line?

•  (+)²–(²+²) = 159
•  ◯³+²+◯ = 159   