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This is a number trail involving ten arithmetical steps. Be careful with your calculations – and no calculators please!

Start with the number 40, then:

  • multiply by 4
  • +10%
  • subtract 15
  • divide by seven
  • add nine
  • 1/2 of this
  • +87
  • double this
  • –96
  • ÷10

What is your final answer?

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

The 1st & 4th columns contain the following fourteen numbers:

3   6   13   20   21   22   27   42   55   56   60   63   72   77

What is the product of the highest number and lowest number?

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The Factors Challenge

Which is the ONLY number below that is not a factor of 330?

2    3    5    6    9    10    11    15

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The Mathematically Possible Challenge

Using 5, 6 and 12 once each, with + – × ÷ available, which FIVE numbers is it possible to make from the list below?

2    3    5    7    11    13    17    19    23    29

#PrimeNumbers

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The Target Challenge

Can you arrive at 330 by inserting 3, 5, 10, 11 and 15 into the gaps below?

  •  ◯×◯×(◯–◯–◯) = 330

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. . . is a Mathelona number puzzle where you must solve all four lines arithmetically by filling the 16 gaps below with digits 0-9.

Each digit 0-9 can only be inserted a maximum of TWICE in the whole puzzle:

◯  +  ◯   =     5     =   ◯  +  ◯
◯  +  ◯   =     3     =   ◯  –  ◯
◯  +  ◯   =    10    =   ◯  ×  ◯
◯  +  ◯   =     1     =   ◯  ÷  ◯

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The 7puzzle Challenge

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

The 5th & 7th columns contain the following fourteen numbers:

5   8   9   11   14   18   24   25   28   32   44   50   66   84

Which THREE numbers above 11 each become a multiple of 7 when 11 is subtracted from them?

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The Factors Challenge

Which is the ONLY number below that is a factor of 329?

3    5    7    9    11    13    15    17

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The Mathematically Possible Challenge

Using 5, 6 and 12 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

1    4    9    16    25    36    49    64    81    100

#SquareNumbers

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The Target Challenge

Can you arrive at 329 by inserting 1, 4, 9, 16 and 25 into the gaps below?

  •  ◯×◯×(◯+√◯)+◯ = 329

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. . . will get you thinking of the 5- and 7-times tables, plus some addition.

What is the total of the first SEVEN whole numbers that have a 5 or 7 as part of their number or are multiples of 5 or 7?

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The 7puzzle Challenge

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

The 5th & 7th columns contain the following fourteen numbers:

5   8   9   11   14   18   24   25   28   32   44   50   66   84

Can you find four different numbers that have a sum of 100?

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The Factors Challenge

Which of the following numbers are factors of 328?

2    3    4    5    6    7    8    9

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The Mathematically Possible Challenge

Using 5, 6 and 12 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

11    22    33    44    55    66    77    88    99    110

#11TimesTable

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The Target Challenge

Can you arrive at 328 by inserting 1, 2, 3, 4 and 5 into the gaps below?

  •  (◯²+◯²)×(◯+◯)×◯ = 328

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. . . is a tricky question that’s a real mouth-watering prospect for the number puzzle enthusiast.

Using the numbers 1, 2, 3, 4 and 5 once each, with + – × ÷ available, it is possible to make the vast majority of numbers in the range 50-100.

For example, to arrive at 50 and 51, you could do:

  • (4+3+2+1)×5 = 50,
  • (4×3–2)×5+1 = 51, and so on . . .

Continuing your calculations, what is the LOWEST number in this range that it is NOT possible to make?

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

The 3rd & 6th columns contain the following fourteen numbers:

4   7   12   15   17   30   35   36   40   49   54   64   80   81

How many square numbers are listed above?

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The Factors Challenge

Which of the following numbers are factors of 327?

7    9    11    13    15    17    19    21    None of them

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The Mathematically Possible Challenge

Using 5, 6 and 12 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

10    20    30    40    50    60    70    80    90    100

#10TimesTable

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The Target Challenge

Can you arrive at 327 by inserting 3, 5, 5, 7 and 7 into the gaps below?

  •  ((◯+◯)²–◯×◯)×◯ = 327

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Only one of the following 2-digit even numbers can be divided exactly by 6. Which one?

26  34  38  44  46  50  56  62  64  74  78  86  98

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

The 3rd & 6th columns contain the following fourteen numbers:

4   7   12   15   17   30   35   36   40   49   54   64   80   81

What is the difference between the highest and lowest multiples of 6?

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The Factors Challenge

Which of the following numbers are factors of 326?

4    6    8    12    14    16    None of them

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The Mathematically Possible Challenge

Using 5, 6 and 12 once each, with + – × ÷ available, which are the only THREE numbers it is possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

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The Target Challenge

Can you arrive at 326 by inserting 1, 2, 3, 4 and 5 into the gaps below?

  •  (◯+◯)³+(◯³×◯²)–◯² = 326

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The Main Challenge

Your task is to arrive at the target number of 22 by adding together five numbers. You are limited to using 1-5, but these can be used any number of times.

Can you find the THREE ways of making 22?

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

The 2nd & 4th columns contain the following fourteen numbers:

2   3   6   10   16   20   33   42   45   48   63   70   72   77

Can you find three groups of THREE different numbers that each have a sum of exactly 100?

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The Factors Challenge

Which of the following numbers are factors of 325?

5     15     25     35     45     55     65     75

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The Mathematically Possible Challenge

Using 5, 6 and 12 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

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The Target Challenge

Can you arrive at 325 by inserting 1, 2, 3, 4 and 5 into the gaps on both lines below?

  •  (◯×◯+◯)×(◯+◯)² = 325
  •  (◯³+◯)×◯×(◯–◯) = 325

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This challenge has been taken from our series of Mathelona number puzzle pocket books.

Can you complete this task so all three lines work out arithmetically when inserting the digits 0 0 1 1 1 2 3 4 5 6 7 and 8 into the 12 gaps below?

◯  +  ◯   =     6     =   ◯  –  ◯
◯  +  ◯   =    15    =   ◯  ×  ◯
◯  +  ◯   =     1     =   ◯  ÷  ◯

. . . and as an added challenge . . .

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

The 2nd & 4th columns contain the following fourteen numbers:

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What is the sum of the multiples of 3?

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The Factors Challenge

Which of the following numbers is NOT a factor of 324?

2     3     4     6     8     9     12     18

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The Mathematically Possible Challenge

Using 5, 6 and 12 once each, with + – × ÷ available, which FIVE numbers is it possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

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The Target Challenge

Can you arrive at 324 by inserting 1, 2, 3, 4 and 5 into the gaps on both lines below?

  •  (◯×◯+◯+◯–◯)² = 324
  •  ◯³×◯×(◯+◯)÷◯ = 324

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Using the numbers 1, 3 and 6 once each, with + – × ÷ available, which one of the following numbers is NOT mathematically possible to make?

2    4    6    8    10    12    15    18    21    24

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

The 1st & 7th columns contain the following fourteen numbers:

5   9   13   21   22   24   27   28   32   50   55   56   60   66

Which two numbers become square numbers when 9 is added to them?

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The Factors Challenge

Which of the following numbers are factors of 323?

3    5    7    9    11    13    15    17    19    None of them

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Using 5, 6 and 12 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

5    10    15    20    25    30    35    40    45    50

#5TimesTable

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The Target Challenge

Can you arrive at 323 by inserting 2, 3, 3, 4 and 4 into the gaps below?

  •  ◯⁴+◯³+◯²–◯×◯ = 323

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You have the same starting number and final answer, both 32, with lots of arithmetical steps in between, but the 10th step is missing! What should it be if it involves an integer?

Start with the number 32, then:

–5  ÷9  +4  ×3  –3  ÷2  ×5  –5  ÷2   ?   ×2  +4  ÷3  ×2  =  32

For the real number puzzle enthusiast, there is another possible step which involves a decimal number. What is it?

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

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Which multiple of 7, when adding 1 to it, becomes a prime number?

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Which is the ONLY number below that is a factor of 322?

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Using 5, 6 and 12 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

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Can you arrive at 322 by inserting 6, 7, 8, 9 and 10 into the gaps below?

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  •   3   7   10
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What is the ONLY target answer from 10-30 that can be made by ALL three combinations?

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

The 5th & 6th columns contain the following fourteen numbers:

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How many more square numbers are listed than cube numbers?

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The Factors Challenge

Which of the numbers below are factors of 321?

3    5    7    9    11    13    None of them

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Using 5, 6 and 12 once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

3    6    9    12    15    18    21    24    27    30

#3TimesTable

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Can you arrive at 321 by inserting 1, 3, 4, 7 and 8 into the gaps below?

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