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The Main Challenge

Can you correctly place 0 1 1 2 2 3 4 5 5 8 9 and 9 into the 12 gaps below?

◯  +  ◯   =    3    =   ◯  –  ◯
◯  +  ◯   =    8    =   ◯  ×  ◯
◯  +  ◯   =    1    =   ◯  ÷  ◯

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The playing board of Buy Qualitest Phentermine is a 7-by-7 grid of 49 different numbers, ranging from 2 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 two numbers have a difference of 25?

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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 ways of making 67 when using Lagrange’s Theorem. Can you find them all?

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Can you arrive at 67 by inserting 4, 5, 7 and 8 into the gaps on each line?

•  ◯×◯+◯×◯ = 67
•  ◯²+◯+◯×√◯ = 67
•  ◯³+(◯+◯)÷◯ = 67

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The Main Challenge

When multiplying two numbers together and then adding or subtracting a third number, there are four ways of reaching 60 when the three numbers used in each calculation are in the range 1-9, and can be repeated.

One way to make 60 is (9×6)+6; can you find the other three?

[Note:  (9×6)+6 and (6×9)+6 counts as just one way.]

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The 7puzzle Challenge

The playing board of Buy Qualitest Phentermine is a 7-by-7 grid of 49 different numbers, ranging from 2 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

How many pairs of consecutive numbers are there?

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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 SIX ways of making 66 when using Lagrange’s Theorem. Can you find them all?

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Can you arrive at 66 by inserting 2, 3, 4 and 9 into the gaps on each line?

•  (◯×◯+◯)×◯ = 66
•  (◯×◯–◯)×◯ = 66
•  ◯²×◯+◯×◯ = 66
•  ◯³+(◯+◯)²+√◯ = 66

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The Main Challenge

You must arrive at the target number of 24 by using four unique numbers from 10-19 and with + – × ÷ available to use; one such example being (15×12÷18)+14 = 24.

Can you derive another 4-number combination to make 24?

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The 7puzzle Challenge

The playing board of Buy Xanax Fast Delivery is a 7-by-7 grid of 49 different numbers, ranging from 2 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

How many cube numbers are present?

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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 ways of making 65 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 65 by inserting 1, 5, 6 and 8 into the gaps on each line?

•  (◯+◯–◯)×◯ = 65
•  ◯×◯+(◯–◯)² = 65
•  ◯²+(◯+◯)÷◯ = 65
•  ◯²+◯–◯×◯ = 65

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The Main Challenge

From the numbers 1-30, eliminate the following:

• numbers containing the digit 1
• prime numbers
• numbers in the 20’s
• factors of 72

What is the only number that remains?

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The 7puzzle Challenge

The playing board of Buy Xanax Fast Delivery is a 7-by-7 grid of 49 different numbers, ranging from 2 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 square numbers?

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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 of making 64 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 64 by inserting 4, 6, 8 and 10 into the gaps on each line?

•  (◯+◯)×(◯–◯) = 64
•  ◯×(◯+◯–◯) = 64
•  ◯²×(◯+◯)÷◯ = 64
•  ◯×(◯–◯)×√◯ = 64

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The Main Challenge

Which is the only digit not represented when listing the square numbers from 10² to 19²?

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The 7puzzle Challenge

The playing board of Buy Xanax Xr Online is a 7-by-7 grid of 49 different numbers, ranging from 2 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

Find three different numbers that have a sum of 100.

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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 ways of making 63 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 63 by inserting 3, 3, 4 and 5 into the gaps on each line?

•  ◯×◯×◯+◯ = 63
•  ◯²×◯–◯×◯ = 63
•  ◯×◯×(◯+√◯) = 63

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The Main Challenge

When listing the FIVE 3-digit cube numbers, all digits from 1 to 9 are represented, except one. Which digit is missing?

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The 7puzzle Challenge

The playing board of Buy Xanax Xr Online is a 7-by-7 grid of 49 different numbers, ranging from 2 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 two multiples of 9?

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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 THREE ways of making 62 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 62 by inserting 2, 4, 6 and 9 into the gaps on each line?

•  (◯+◯)×◯+◯ = 62
•  (◯+◯)×◯–◯ = 62
•  (◯+◯)×◯+◯² = 62

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The Main Challenge

Read the information below to find each of these three different numbers:

•  A is the only 2-digit square number that does not contain any odd digits
•  B is the only 2-digit prime number with both its digits the same
•  C is the only 2-digit cube number less than 50

Calculate the sum of A, B and C.

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The 7puzzle Challenge

The playing board of Buy Xanax Xr Online is a 7-by-7 grid of 49 different numbers, ranging from 2 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 even numbers listed?

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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 ways of making 61 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 61 by inserting 3, 5, 8 and 10 into the gaps on each line?

•  ◯×◯+◯+◯ = 61
•  (◯–◯)×◯+◯ = 61
•  (◯+◯)×◯+double◯ = 61
•  (◯+◯)×◯–half◯ = 61

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The Main Challenge

Happy St David’s Day/Dydd Gŵyl Dewi Hapus.

It’s our National Day in Wales today so try our special alphabet number puzzle; probably the hardest you can ever try!

The longest place name in the UK is a small village on the island of Anglesey. When allocating each letter of the English alphabet a numerical value, A=1 B=2 C=3 … Z=26 and adding the individual letters, what is the total value of  LLANFAIRPWLLGWYNGYLLGOGERYCHWYRNDROBWLLLLANTISILIOGOGOGOCH?

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The playing board of Buy Xanax Xr Online is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 4th & 6th rows contain the following fourteen numbers:

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Which two numbers, when each is tripled, are also on the list?

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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 THREE ways of making 60 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 60 by inserting 2, 3, 4 and 7 into the gaps on each line?

•  (◯+◯)×(◯+◯) = 60
•  (◯–◯)×◯×◯ = 60
•  ◯²+◯²+◯–◯ = 60
•  ◯²×◯²+◯–◯ = 60

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The Main Challenge

Your starting number is 18 and your task is to arrive at the same final answer.  There are ten arithmetical steps from beginning to end, each one involving a whole number, but the 9th (and penultimate) step is missing!  What must it be?

÷2   +3   –8   ×6   +4   –3   ÷5   ×2   ?   ×2   =   18

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The 7puzzle Challenge

The playing board of Buy Xanax Xr Online is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 4th & 6th rows contain the following fourteen numbers:

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What is the difference between the lowest and highest multiples of 4?

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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 THREE ways of making 59 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 59 by inserting 4, 5, 6 and 10 into the gaps on each line?

•  ◯×◯+◯–◯ = 59
•  ◯²+◯×◯+◯ = 59
•  (◯+◯)×◯–◯ = 59

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The Main Challenge

Starting from 1, find the sum of the first SEVEN whole numbers that do not contain a 3, 5 or 7 as part of their number, nor are multiples of 3, 5 or 7.

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The playing board of Buy Qualitest Phentermine is a 7-by-7 grid of 49 different numbers, ranging from 2 up to 84.

The 4th & 6th rows contain the following fourteen numbers:

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What is the sum of the multiples of 11?

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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 FIVE ways of making 58 when using Lagrange’s Theorem. Can you find them?

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Can you arrive at 58 by inserting 4, 6, 8 and 10 into the gaps on each line?

•  ◯×◯–◯÷◯ = 58
•  ◯²+◯+◯+◯ = 58
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