## DAY/DYDD 252: T he Main Challenge

Can you complete this task so the three lines work out arithmetically when inserting the digits 1 1 2 2 3 3 4 5 6 7 8 and 9 into the 12 gaps below?

◯  +  ◯   =     7     =   ◯  –  ◯
◯  +  ◯   =    12    =   ◯  ×  ◯
◯  +  ◯   =     4     =   ◯  ÷  ◯

Further details of our pocket book of challenges can be found by clicking Mathelona. 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 2nd & 6th rows of the playing board contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

How many pairs of consecutive numbers are listed? The Factors Challenge

Which of the following numbers, if any, are factors of 252?

3    4    5    6    7    8    9    10    11    None of them

[ Today’s Hint: A multiple of 9 will always have its digits adding up to 9, 18, 27… ] The Mathematically Possible Challenge

Using 58 and 11 once each, with + – × ÷ available, which are the ONLY two 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 252 by inserting 3, 5, 7, 9 and 11 into the gaps below?

•  (◯+◯)×◯×◯²÷◯ = 252 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 251: The Main Challenge

Here’s a special 24game-type challenge with a difference.

Using the numbers 1, 3, 4 and 6 once each, together with + – × ÷ available, it is possible to make lots of different target numbers, not just 24.

For instance:

• to make 1: (3+4–6)×1 = 1
• to make 2: (3+4–6)+1 = 2
• to make 3: (6–4–1)×3 = 3 . . . and so on.

Using the same four numbers, can you make the target numbers 6, 12, 18 and 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 2nd & 6th rows of the playing board contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

What is the sum of the multiples of 5? The Factors Challenge

Which of the following numbers, if any, are factors of 251?

2    3    4    5    6    7    8    9    10    None of them

[ Today’s Hint: An even number cannot divide exactly into an odd number ] The Mathematically Possible Challenge

Using 58 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 251 by inserting 10, 20, 30, 40 and 50 into the gaps below?

•  (quarter of ◯)×◯–((◯+◯)÷◯)² = 251 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 250: The Main Challenge

The following clues are given to help you find a particular number:

• I am a 2-digit number
• my two digits have a difference of one
• I am a multiple of 7
• the number immediately below me is a prime number

Who am I? 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 & 4th rows of the playing board contain the following fourteen numbers:

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

How many multiples of 4 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 SEVENTEEN different ways to make 250 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 58 and 11 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 250 by inserting 5, 10, 15, 20 and 25 into the gaps below?

•  ◯×◯–(◯²+◯+◯) = 250 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 249: The Main Challenge

Here’s a challenging number trail question involving seven arithmetical steps.  Start with the number 139, then:

8     +103     decrease by 50%     37     +109     1/3 of this     ÷7     =     ? 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 & 4th rows of the playing board contain the following fourteen numbers:

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

How many pairs of numbers have a sum of 75? 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 249 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 58 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 249 by inserting 1, 2, 3, 4 and 5 into the gaps below?

•  (◯×◯÷◯)–√◯ = 249 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 248: The Main Challenge

What is the lowest Prime Number total it is possible to achieve when adding together SEVEN unique non-Prime Numbers? 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 & 4th rows of the playing board contain the following fourteen numbers:

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

What is the sum of the factors of 40? 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 just THREE different ways to make 248 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

2    4    6    8    10    12    14    16    18    20

#EvenNumbers The Target Challenge

Can you arrive at 248 by inserting 5, 7, 8, 10 and 12 into the gaps below?

•  ◯³+√(◯+◯+◯)–◯² = 248 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 247: The Main Challenge

Can you complete our Mathelona puzzle by placing the 12 digits below into the 12 gaps so all three lines work out arithmetically?

0     1     2     2     3     3     4     5     6     7     8     9

◯  +  ◯   =     3     =   ◯  –  ◯
◯  +  ◯   =    10    =   ◯  ×  ◯
◯  +  ◯   =     9     =   ◯  ÷  ◯

Further details of our pocket book of challenges can be found by clicking Mathelona. 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 & 4th rows of the playing board contain the following fourteen numbers:

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

Which pair of numbers have a difference of 9? 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 247 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 25 and 10 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 The Target Challenge

Can you arrive at 247 by inserting 3, 4, 5, 6 and 7 into the gaps below?

•  (◯+◯)×◯×◯–◯ = 247 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 246: The Main Challenge

The seven musical letters, A-G, in the three sections below each contain an addition calculation. Only one letter has the same answer in all three sections, which one?

• Section 1

E: 11+6    G: 7+7    C: 10+4    A: 13+6    B: 9+4    F: 8+8    D: 9+3

• Section 2

A: 11+5    C: 13+5    F: 9+6    E: 15+3    D: 6+6     B: 8+5    G: 7+6

• Section 3

C: 11+3    B: 11+2    D: 7+4    G: 14+1    F: 12+3    E: 14+3    A: 15+4 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 & 4th rows of the playing board contain the following fourteen numbers:

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

Which two separate numbers, when 9 is added to them, both become 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 are FOURTEEN different ways to make 246 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which FOUR 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 246 by inserting 3, 4, 5, 6 and 7 into the gaps below?

•  (◯×◯+◯×◯)×◯ = 246 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 245: The Main Challenge

Using the numbers 5, 5 and 10 once each, with + – × ÷ available, list the NINE 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 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

Which four different numbers have a sum of 100? 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 245 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

15    30    45    60    75    90    105    120    135    150

#15TimesTable The Target Challenge

Can you arrive at 245 by inserting 1234 and 5 into the gaps below?

•  (◯+◯)²×◯×(◯–◯) = 245 Answers can be found here. Click Paul Godding for details of online maths tuition. ## DAY/DYDD 244: The Main Challenge

Consider all odd numbers from 1 to 25.

Eliminate all single-digit numbers, square numbers and multiples of 7 as well as numbers that have their two digits adding up to an even number.

Which number is the only one remaining? 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 & 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

From the list, what is the sum of the multiples of 4? 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 244 when using Lagrange’s Theorem. How many can you find? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

13    26    39    52    65    78    91    104    117    130

#13TimesTable The Target Challenge

Can you arrive at 244 by inserting 4, 9, 16, 25 and 36 into the gaps below?

•  (◯+◯)×√◯×√◯–√◯ = 244 Answers can be found here. Click Paul Godding for details of online maths. ## DAY/DYDD 243: The Main Challenge

We invite you to use seven 3’s (3 3 3 3 3 3 and 3) once each, with + – × ÷ available, to make various target numbers.

For instance, to make 1 and 2, you could do:

• 3 × (3÷3) – (3÷3) – (3÷3)  =  1
• (3+3) × (3÷3) × (3÷3) ÷ 3 =  2  . . .  and so on.

Continuing, as above, can you make the target numbers from 3 to 6? 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 & 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

Find three different numbers from the list that have a sum of 100. 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 243 when using Lagrange’s Theorem. How many of them can you find? The Mathematically Possible Challenge

Using 25 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

12    24    36    48    60    72    84    96    108    120

#12TimesTable The Target Challenge

Can you arrive at 243 by inserting 2, 3, 4, 5 and 6 into the gaps below?

•  ◯×(◯+◯)²+(◯+◯)² = 243 Answers can be found here. Click Paul Godding for details of online maths tuition. 