# Challenge Math and Brain Teaser Problems!

#1

Hello! Any of you like doing HARD brain teasers and math? Here, Hops can post challenges and have other Hops solve it! Hope you all enjoy!

@Liza
@Rodrigo
@asha, feel free to participate!

Nerdy Maths topics [check 'em out here!]
Hopscotch Programming Puzzles
#2

What is the problem?

#3

First challenge!

1) Find the sum of all prime numbers that are less than 100 and contain a digit of 5.

Due in a day! Good luck!

#5

117...? idk.

#6

117
That was easy XD

#7

NindroidGames was a little TOO fast! He's the winner! He can get a request. I'll get a harder one.

#8

Second challenge!
What number is the question mark?!

#9

The number six

6

I think

#10

Might be a good idea to put your answers in the [spoiler] tag so other people won't see it @Sweetlina @DECODECO

#11

6
Magic square time

#12

Ok, I'm a gonna join (this is a good one)

Since the only one prime ends in a 5, which is 5, there are no other primes less than 100, except for the ones from 50 - 59. 53 and 59 happen to be prime.

So.. 53 + 59 + 5 = 117

Great question!

#13

Ooh! I've got a question!

What is the summation of the reversal of all square numbers?

This is what you'll need to do
Ex) 1/1 + 1/4 + 1/9 + 1/16 + 1/25...

Is there an easy way to write this??

Hint: No, it does not diverge to infinity

Give a proof to why the summation of the reversal of every number does diverge to infinity:

Ex) 1/1 + 1/2 + 1/3 + 1/4 + 1/5..

Why does it go to infinity?

#14

Aren't there endless square numbers?

#15

Maybe it approaches something?
Edit: oh whoops I was browsing through the Numberphile topic then saw @JonnyGamer posted the answer I wouldn't have found that though, although can still try .

This is a great topic too!

#16

Oh, lol, whoops. I should probably put all the answers to problems in details form now on

#17

Oh, no it's fine! I think you can just discuss anyway.

#18

More math fun! Here's a new challenging Geometry/Trig problem!
The circle is inscribed inside an equilateral triangle that has a side length of one. Find the blue shaded area:
I'm using this for a new constant I'm going to invent!

Yes, my iPad battery is at 11% right now, I should probably charge

Hint! Might be needed..

The height of the circle is 2/3 of the height of the triangle. This helps.
Also, copy this on scratch paper. You're gonna be using a lot of pi and square roots

#19

Ooh thanks for sharing this

Hmm okay I started before you put up the hint, I got something like `(3√3 - π)/36` but I'm going to check over things...

#20

All you need to check is to multiply the answer by 3, and add the area of the circle. Hopefully that will add up to the area of the entire triangle

Yeah, I created this in the morning and the answer was over 12 instead of yours, so I thought I had messed up at the beginning and got super frustrated I was second guessing myself a lot when I was trying to find the height of the triangle, since I wasn't allow to use my iPad at the time. I realized I should've cut the triangle in half to use the 30-60-90 theorem..

(I'm having a friend of mine do the problem at the same time as you, so if they're both the same, most likely the answer will be right)

Also, I'll attach an image:

I'm gonna find the empty space of the triangle not taken up my the circles to create a mathematical constant. There's probably a function or summation used to find it, though

#21

Ooh okay mathematical investigation! ️‍♀️
That's a great way to check! – would not have thought about that.

Here is a more processed version of my working out: