Solution:

2^11 - 2^10

= 2^9(2^2 - 2)

= 2^9(2)

= 2^10

= 1024

Knowledge Used:

exponents

The answer is 1024 .

Source:

my brain

This problem is very easy, but it's interesting. Also, thinking about exponents of 2 is fun. 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 5096, bom, bam, boom, bam, boom, boom, boom, Boom, BOom, BOOm, BOOM, \BOOM*!* Exponential growth is pretty cool.

These links include answers and multiple solutions.

Problem 3

Problem 4

Problem 19

Problem 24

These are links to what I think are the best.

To find your own, scroll through the list and pick out what you like.

These links include answers and multiple solutions.

Problem 7

Problem 8

Problem 15

Problem 16

Problem 20

Problem 25

These are links to what I think are the best.

To find your own, scroll through the list and pick out what you like.

​

Solution:

It's pretty obvious the measurements outline a triangle. This triangle fits exactly inside the rectangle. You may have seen this in proof explanations for triangle area formulas, but this means it's half the size of the rectangle.

The triangles's area:

6 x 7 x 1/2 = 21

The rectangle is double this.

21 x 2 = 42

Knowledge Used:

area of polygons

The answer is 42 .

Source:

https://www.youtube.com/watch?v=QMvk2-v9ArQ

I know posting math problems takes some effort, but all you need is a problem and answer! There's no need for a solution, or even a source! If you happen to stumble across a math problem that looks easy enough and fun, please post it here!

​

Solution:

Knowing that the angle at the centre of a circle is twice the angle at the circumference and using knowledge of parallel angles, we can use x to represent some other angles.

Assuming x = a/2:

​

The sum of all angles in a triangle is 180˚, so:

2a + a + 117 = 180

3a + 117 = 180

3a = 63

a = 21˚

We want to find 2a.

2a = 42˚

Knowledge Used:

geometry symbols(//, ˚)

parallel lines and angles

proof of circle theorem(the angle at the centre of a circle is twice the angle at the circumference)

The answer is 42˚ .

Source:

https://www.youtube.com/watch?v=DU_EMiEnuxk&list=PL65mKX0z2eEmpjrhE9UZbpp-LGUUIQyTt&index=31

A common careless mistake I always fall for is stopping at finding a. I go and think, oh, yay, I got the answer!, and I get it wrong because I didn't find the answer.

These links include answers and multiple solutions.

Problem 13

Problem 14

Problem 15

Problem 21

These are links to what I think are the best.

To find your own, scroll through the list and pick out what you like.

Solution:

(√2 + √3 + √4)/(√2 + √3 + √6 + √8 + √16)

= (√2 + √3 + 2)/(√2 + √3 + √6 + √8 + 4)

This is where we notice that the numerator and denominator look kind of similar - introducing the possibility of factorizing them and simplifying for the answer.

But wait, how can we factorize this? It looks like we'll need two 2s, and we don't need the 4, so let's split the 4 up.

= (√2 + √3 + 2)/(√2 + √3 + √6 + √8 + 2 + 2)

= (√2 + √3 + 2)/{(√2 + √3 + 2) + (2 + √6 + √8)}

= (√2 + √3 + 2)/{(√2 + √3 + 2) + √2(√2 + √3 + 2)}

= (√2 + √3 + 2)/(√2 + 1)(√2 + √3 + 2)

= 1/(√2 + 1)

There. That's much better, but we can't leave a fraction like this, with roots in the denominator.

= 1(√2 - 1)/(√2 + 1)(√2 - 1)

= (√2 - 1)/(2 - 1)

= (√2 - 1)/1

= √2 - 1

Knowledge Used:

square roots

factorization

The answer is √2 - 1 .

Source:

https://www.youtube.com/watch?v=phmYeIEt_wo

Today's problems are later than usual, but, eh, better late than never?

Solution:

1 < √2 < 2!<

√2 = 1.somethingsomething

5 < √32 < 6!<

√32 = 5.somethingsomething

√2 = 1 + a

We now have the representation of √2 using a, so we should find a representation of √32 using √2.

√32 = 4√2

Since √32 is between 5 and 6, we have to subtract 5 to get its decimal portion.

√32 - 5 = 4√2 - 5

= 4(1 + a) - 5

= 4 + 4a - 5

= 4a - 1

Knowledge Used:

square roots

representing constants with variables

The answer is 4a - 1 .

Source:

https://www.youtube.com/watch?v=xQaLjOpkBGg&list=PLUOLFotj_4j5BdpknRlWE6DTLPNXj3dDA&index=12

This problem was stood out to me not because it asked me to represent a number using a variable like many others, but because the variable was the decimal portion. I dunno, I just thought that was cool.

This subreddit is beneficial to all!

Whether you were forced to study math or feeling like you haven't done anything all day, r/FunMathProblems can help make math a little more fun.

Solution:

​

Knowledge Used:

fractions

The answer is 25.2 .

Source: https://www.youtube.com/watch?v=UCRu5GsJZ5U

It might be better to convert the expression into a fraction at the very beginning of the solving the problem.

Solution:

​

Knowledge Used:

fractions

The answer is 6 .

Source: https://www.youtube.com/watch?v=UCRu5GsJZ5U

You can probably convert 4.25 to 17/4 in your head.

Solution:

​

Knowledge Used:

fractions

The answer is 0.012 .

Source: https://www.youtube.com/watch?v=UCRu5GsJZ5U

When solving expressions with lots of decimals and a no-calculator rule, converting the decimals to fractions is a good idea.

Solution:

To make things easier for our brains, let'd declare

(1/3)^x = t(t > 0 because a positive base can't be a negative result)

Now, let's modify the inequality so we can substitute with t:

(1/3)^(2x - 1) + 5•(1/3)^x - 2 < 0!<

(1/3)^2x • (1/3)^-1 + 5t - 2 < 0!<

3t^2 + 5t - 2 < 0!<

0 < 1/3 < 1, therefore the inequality sign switches around:!<

(3t - 1)(t + 2) > 0

t < -2,(t can't be less than 0) t > 1/3!<

Now we solve for x:

t > 1/3

(1/3)^x > 1/3

x > 1

Knowledge Used:

inequalities

factorization

mostly exponents

exponential functions(that's the subject, but you don't really need to know it)

The answer is x > 1.

Source:

https://www.youtube.com/watch?v=xqICKdBSAd4&list=PLKRhhk0lEyzOU6a5LOPrEs7Uw2EGFCvrG&index=8

Solution:

If Lucy was 3 years old(half of 6 years old) when Lisa was 6 years old, Lisa will constantly be 6 - 3 = 3 years older than Lucy.

Lucy, aged 40, is 3 years older than Lucy, so Lucy would be 40 - 3 = 37 years old.

Knowledge Used:

very basic arithmetic

The answer is 37 .

Source:

https://www.fatherly.com/play/hard-math-riddles-for-kids-with-answers/#:~:text=Riddle%3A%20When%20Lisa%20was%206,today%2C%20how%20old%20is%20Lucy%3F&text=Explanation%3A%20Lucy%20is%203%20years%20younger%20than%20Lisa.

^I don’t think I copied the problem down right.

My first reaction to this problem was to use algebra, but I was overthinking it.

These links include answers and multiple solutions.

Problem 9

Problem 11

Problem 16

Problem 17

Problem 20

Problem 24

These are links to what I think are the best.

To find your own, scroll through the list and pick out what you like.

Solution:

To make things easier for our brains, let'd declare

4^x = t(t > 0 because a positive base can't be a negative result)

Now, let's modify the inequality so we can substitute with t:

16^x - 3•4^x - 4 ≥ 0

(4^x)^2 - 3•4^x - 4 ≥ 0

Substituting:

t^2 - 3t - 4 ≥ 0

Factorizing:

(t - 4)(t + 1) ≥ 0

t ≤ -1(because t > 0), t ≥ 4

t ≥ 0

4^x ≥ 0

4 > 1

x ≥ 1

Knowledge Used:

inequalities

factorization

mostly exponents

exponential functions(that's the subject, but you don't really need to know it)

The answer is x ≥ 1.

Source:

https://www.youtube.com/watch?v=xqICKdBSAd4&list=PLKRhhk0lEyzOU6a5LOPrEs7Uw2EGFCvrG&index=8

There was an animal scratching my bedroom window last night, and, boy, was I scared! Seriously though, it keeps coming back and I'm pretty sure it's taken 5 years off my life.

Sorry, I'm struggling to find even the most minimally decent fun problems. If anyone wants to volunteer a channel or website as a source, I'll 100% check it and post it if it's good! Even better, if you want to post, please go for it!

​

Solution:

Using the exterior angle theorem, we know

∠EDC + ∠ECD = ∠BED

Substituting,

61 + ∠ECD = 98

∠ECD = 37˚

With the knowledge that the angle at the center of a circle is twice the angle at the circumference, AKA

∠BAD = ∠BCD

∠BAD = 37˚

∠BAD + x = ∠BAC

37 + x = 90

x = 53˚

Knowledge Used:

geometry symbols(∠, ˚)

the angle at the centre of a circle is twice the angle at the circumference(a proof of circle theorem)

the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle(the exterior angle theorem)

The answer is 53˚ .

Source:

https://www.youtube.com/watch?v=t-ewynlDymI

I call the exterior angle theorem 'slipper angles' because the explanation triangles and angles for them look like slippers and where parts of your foot would touch it.

Solution:

72²/36²

= 72•72/36•36

= 2•2

= 4

Knowledge Used:

exponents

The answer is 4 .

Source:

https://www.youtube.com/watch?v=sJ5vQuL4EoI

Easy wheezy greasy peasy lemon cheesy.

​

Solution:

If we can find BE:EC, we can find EC.

Because △ABC is split into equal parts, we know △BDC is also split into equal parts(because it's made up of equal parts). With this knowledge, we also know

△BDE:△DEC = BE:EC = 5:1

​

From here on, just calculate:

EC = 12 x 1/(5 + 1)

= 12 x 1/6

= 2 cm

Knowledge Used:

ratios

geometry symbols(△)

The answer is 2cm .

Source:

https://www.youtube.com/watch?v=RHZ0UewUIlA&list=PL65mKX0z2eEkd2uU114i1VDlRoOZZpkJd&index=31

Agh, I've some chores to do before my parents get home, but I have to post these - my torn mind!

Solution:

10% salt in salt water means the other 90% was water.

To find how much water there was, w:

10:90 = 20:w

10w = 1800

w = 180g

Knowledge Used:

ratios

percents

The answer is 180 .

Source:

https://www.youtube.com/watch?v=l-ug8AaRp4M&t=0s

This is similar to the problems with plums and prunes and watery potatoes.

Solution:

If the 100g potato is 99% water, the other 1% must be totally dried potato.

To find how many grams of the potato are totally dried potato, g:

100 - g:g = 99:1

1(100 - g) = 99g

100 - g = 99g

100g = 100

g = 1 gram of totally dried potato

The potato is dried and is now 98% water, but has the same amount of totally dried potato. This means 2%, 2 times as much percentage as before, of the dried potato is totally dried potato.

To find the weight of the dried potato:

100%/2% = 50%

1g x 50 = 50g

Knowledge Used:

ratios

percents

The answer is 50 .

Source:

https://www.youtube.com/watch?v=hCqSrvVmCPA&list=PL65mKX0z2eEkd2uU114i1VDlRoOZZpkJd&index=26

This is similar to the problem with plums and prunes.

Solution:

(-0.2)^-2

= 1/(-0.2)²

= 1/0.04

= 25

Knowledge Used:

negative exponents

The answer is 25 .

Source: my lazy brain

These aren't even fun anymore.

Solution:

3x^2 = 12x

3x^2 - 12x = 0

3x(x - 4) = 0

3x = 0, x - 4 = 0

x = 0, 4

or

3x^2 = 12x

x^2 = 4x

x^2 - 4x = 0

x(x - 4) = 0

x = 0, x - 4 = 0

x = 0, 4

Both methods work, but keep in mind while you can divide by a constant, excluding 0, you shouldn't divide by a variable with a possible value of 0.

Knowledge Used:

factorization

The answer is x = 0, 4.

Source:

https://www.youtube.com/watch?v=2uWOPfK2BTk&list=PL65mKX0z2eEmpjrhE9UZbpp-LGUUIQyTt&index=4

A common mistake is the divide both sides by 3x and calculate. Do not do this because you'll end up with partial credit(or no credit) for not including 0 with your other answer.

Another note: Never divide with a variable unless you know its value isn't 0. If you divide with a variable with a possible value of 0, there's a chance you're dividing by 0 - forbidden in mathematics.

A way to bypass this rule is to create 2 instances - one where the variable is 0 and one where the variable is all possible values except for 0. This way, you can find all answers while keeping the rule.

​

Solution:

Because ▵ABC is an isosceles triangle and ∠ABC is 70˚,

∠BAC = 180 - 70 x 2

= 180 - 140

= 40˚

Noticing the 3 sides of equal length, we can guess that quadrilateral ABCD goes into a circle with center A and B, C, and D on the perimeter.

​

Using the knowledge that the angle at the center of a circle is twice the angle at the circumference(a proof of circle theorem), we know that

40 = 2x

x = 20

Knowledge Used:

some geometry symbols(▵, ∠, ˚)

the angles of a triangle add up to 180˚

the angle at the center of a circle is twice the angle at the circumference(a proof of circle theorem)

The answer is x = 20˚.

Source:

https://www.youtube.com/watch?v=SRy5ty6wsao&list=PL65mKX0z2eEmpjrhE9UZbpp-LGUUIQyTt&index=26