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The Main Challenge

Here’s seven more mental arithmetic questions to try. Can you get all seven correct?

(11 – 5) – (4 + 1) = ?
What is 10 more than –4?
47 × 4 = ?
0.32 ÷ 4 = ?
3/4 × 2/3 = ?
Which one is bigger: 2 cubed or 3 squared?
You wish to buy two £30 items. Which offer would give you the best deal: (A) 15% off both items, (B) 2nd item is 40% off, (C) get 1/3 off the 2nd item, (D) 25% off 1st item, 10% off 2nd item.

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 1st & 2nd rows contain the following fourteen numbers:

2 8 9 14 15 17 22 28 40 48 55 63 64 72

From the list, find TWO numbers that have a sum of 111.

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 SEVEN ways of making 108 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 1, 4 and 9 once each, with + – × ÷ available, which THREE numbers is it 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 108 by inserting 2, 3, 5 and 11 into the gaps on both lines?

◯²×◯²+◯–◯ = 108
◯×◯²+◯²+◯ = 108

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The Main Challenge

Here’s seven tricky mental teasers to try:

(18 – 5) – (7 – 17) = ?
128 + 294 = ?
How many seconds are in a quarter-of-an-hour?
How many degrees are in three-quarters of a circle?
(16 – 8) × (13 – 8) = ?
On four consecutive days, you spend £55, £74, £36 and £15. What is the average amount spent per day?
What is 15% of £8?

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 1st & 2nd rows contain the following fourteen numbers:

2 8 9 14 15 17 22 28 40 48 55 63 64 72

Which two numbers have a difference of 42?

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 107 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 1, 4 and 9 once each, with + – × ÷ available, which FOUR 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 107 by inserting 9, 10, 11 and 12 into the gaps on both lines?

◯×◯+◯–◯ = 107 (2 different ways!)
◯×◯+(◯–◯)³ = 107

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The Main Challenge

Here are seven more mental arithmetic questions for you to try:

Which number multiplied by itself gives 196?
What is 50 + 400 + 5?
54 – 45 = ?
If Jo runs 10 miles in one hour, how much further would she get in an extra 15 minutes running at the same rate?
(14 – 3) × (7 + 2) = ?
Which fraction comes next in the list: 1/12, 1/6, 1/4, 1/3, …
How many days equal 6 weeks?

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 1st & 2nd rows contain the following fourteen numbers:

2 8 9 14 15 17 22 28 40 48 55 63 64 72

List FIVE different numbers that total 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 SEVEN ways of making 106 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 1, 4 and 9 once each, with + – × ÷ available, which FIVE 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 106 by inserting 4, 5, 6 and 7 into the gaps on both lines?

◯²+◯²+◯²+◯ = 106
◯³–(◯+◯)×double◯ = 106

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The Main Challenge

How quickly can you correctly answer the following seven questions?

(17 – 4) + (12 – 9) = ?
(3 – 2) – (16 – 16) = ?
What is two-thirds plus three-quarters?
109 + 10 = ?
(3 + 16) + (16 + 9) = ?
(11 – 5) + (4 + 1) = ?
What is the perimeter of a 13cm by 13cm square?

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 2nd & 5th rows contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

Which two numbers in the list are cube 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 SIX ways of making 105 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 1, 4 and 9 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

The Target Challenge

Can you arrive at 105 by inserting 5, 5, 6 and 10 into the gaps on both lines?

◯×(◯+◯)–◯ = 105
◯²+◯–◯÷◯ = 105

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The Main Challenge

Here’s another selection of mental arithmetic questions. Can you answer all seven correctly?

(10 + 10) – (15 – 3) = ?
What is the sum of 0.83 and 0.89?
What is 1 × 9?
If Ben earns £10 every half-hour, how much will he earn in 40 hours?
If you burn 100 calories by climbing 100 stairs, how many calories would you burn when climbing 50 stairs?
What is 5,456 – 4,372?
Twice my age plus 4 more is 72. How old am I?

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 2nd & 5th rows contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

What is the product of the two prime 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 just THREE ways of making 104 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 5, 7 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is NOT possible to make from the list below?

25 35 45 55 65 75 85 95 105 115

#MultiplesOf5

The Target Challenge

Can you arrive at 104 by inserting 2, 4, 12 and 15 into the gaps on both lines?

(◯–◯)×(◯–◯) = 104
◯×(◯+◯)–◯² = 104

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The Main Challenge

Here’s a 7-part challenge to test your basic arithmetic knowledge:

What is 56 divided by 14?
(1 + 11) + (20 – 4) = ?
Find which one of these is a factor of 14. Is it 3, 5, 7 or 10?
What is the next number? 15, 30, 45, 60, …
10,000 × 0.001 = ?
(2 + 3) – (4 – 9) = ?
What is the sum of 0.81 and 0.5?

Can you get 7 out of 7 correct?

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 2nd & 5th rows contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

Find THREE sets of three different numbers 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 FIVE ways of making 103 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 5, 7 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

50 51 52 53 54 55 56 57 58 59

#NumbersIn50s

The Target Challenge

Can you arrive at 103 by inserting 1, 2, 6 and 8 into the gaps on both lines?

◯²+◯²+◯²–◯² = 103
(◯+◯+◯)²–half(◯²) = 103

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The Main Challenge

Can you place the 16 numbers 0 0 1 1 2 2 3 4 4 5 6 7 7 8 9 9 into the 16 gaps below so all four lines work out arithmetically?

◯ + ◯ = 9 = ◯ + ◯
◯ + ◯ = 7 = ◯ – ◯
◯ + ◯ = 12 = ◯ × ◯
◯ + ◯ = 6 = ◯ ÷ ◯

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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 2nd & 5th rows contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

What is the sum of the 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 SEVEN ways of making 102 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 5, 7 and 10 once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

40 41 42 43 44 45 46 47 48 49

#NumbersIn40s

The Target Challenge

Can you arrive at 102 by inserting 3, 4, 6 and 10 into the gaps on both lines?

(◯+◯+◯)×◯ = 102
◯²+◯×◯÷◯ = 102

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The Main Challenge

Using each of the numbers 0.5, 1, 1.5 and 2 once each, with the four arithmetical operations + – × ÷ available, can you arrive at the target answer of 7?

For the number puzzle enthusiast, can you find a 2nd way of making 7?

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 2nd & 5th rows contain the following fourteen numbers:

6 7 8 16 17 21 28 48 50 55 63 64 81 84

Which THREE numbers, when 19 is added to each of them, 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 FIVE ways of making 101 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 5, 7 and 10 once each, with + – × ÷ available, which TWO numbers it is 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 101 by inserting 5, 8, 10 and 11 into the gaps on each line?

◯×◯–(◯–◯)² = 101
(◯+◯)×◯+◯ = 101
◯×◯+◯+double◯ = 101

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The Main Challenge

Starting from ONE, what is the 7th whole number, when written in English, that does NOT contain the letter ‘E’?

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 1st & 3rd rows contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

List THREE sets of four different numbers that all have a sum of 200, and THREE sets of three different numbers that all 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 SEVEN ways of making 100 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 5, 7 and 10 once each, with + – × ÷ available, which TWO numbers it is possible to make from the list below?

2 3 5 7 11 13 17 19 23 29

#PrimeNumbers

The Target Challenge

Can you arrive at 100 by inserting 4, 5, 8 and 10 into the gaps on each line?

◯×◯+◯×◯ = 100
(◯+◯÷√◯)×◯ = 100
◯²×(◯+◯–◯) = 100
(◯³÷◯)×◯÷◯ = 100
◯²×(◯+◯–◯)² = 100
(◯×◯+◯)×√◯ = 100
((◯×◯)÷(◯–◯))² = 100

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The Main Challenge

Read the following ten clues about a particular number:

it’s less than 100,
it’s one more than a multiple of 3,
exactly one of its two digits is prime,
you get a prime if you reverse its digits,
it’s not a multiple of 5,
it’s not a prime number,
it has exactly four factors,
it’s not a square number,
the sum of its digits is prime,
if you multiply it by 5, the answer is greater than 100.

Can you find the mystery number?

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 1st & 3rd rows contain the following fourteen numbers:

2 9 13 14 15 22 25 36 40 42 45 66 72 80

How many multiples of 12 are on the list?

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 99 when using Lagrange’s Theorem. Can you find them all?

The Mathematically Possible Challenge

Using 5, 7 and 10 once each, with + – × ÷ available, which 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 99 by inserting 2, 3, 5 and 9 into the gaps on each line?

(◯×◯+◯)×◯ = 99
◯×◯×◯+◯² = 99
(◯+◯)²+◯–◯² = 99
◯²×◯²–◯²÷◯ = 99

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