brainteasers

24 I think

EDIT: I change Answer: 30

think it's 31

It's either 25 if there is a room in the pyramid if no room then it has to be 30 as Rayden said....one assumes a square pyramid.

the question is inaccurate
it is not 100% clear what is meant

it requires 30 balls to form such a pyramid in theory if full, 25 if hollow, but actually the picture is only showing 16 balls

got it 98% shore
think it's 40
just make the pyramid in your head

shouldnt it be 30 balls?

i don't think we can know for shore how meny balls there are.

im not sure how you get to 40

first layer is 4 rows 4 colums = 16 balls
2nd layer is 3x3 = 9 balls
3rd layer is 2x2 = 4 balls
4th layer is 1 ball

16 + 9 + 4 + 1 = 30
That of course if we are talking about a full pyramid of balls and not a pyramid consisting just of an outer shell.

According to my calculations,
1) if the pyramid is rectangular (each ball leans on 4 balls from the layer below), then the k-th layer from top has N[k]=k^2 balls;
2) if the pyramid is hexagonal (each ball leans on 3 balls from the layer below and the first 3 layers have 1, 3 and 7 balls), then the k-th layer from top has N[k]=N[k-2]+3*(k-1) balls at k=2,3,4.... and N[0]=0, N[1]=1;
3) if the pyramid is triangular (each ball leans on 3 balls from the layer below, the first 3 layers have 1, 3 and 10 balls, and each following layer is a triangle), then the k-th layer from top has
N[k]=(9k^2-1)/8 balls when k is an odd number,
N[k]=(9k^2-6k)/8 balls when k is an even number.

The picture shows the 1st case, so there must be 1+4+9+16=30 balls.
A 4-layer hexagonal pyramid would require 23 balls, and a triangular one 29 balls.

You can take some coins and build different pyramids to check

And if we want to go higher...

My roommate has outwitted me again He offered a more optimal pattern for triangular pyramid, where N[k]=k*(k+1)/2, and the first 4 layers have 1, 3, 6 and 10 balls.
Here is the updated plot:

Sorry for triple posting. This task was a real brain teaser and made us busy for some hours

☆hi all
A search for the solution
Turned up the following.

Hello Ringotwin
I think the lower right corner of the 2nd picture is not incorrect solution - it is just another way to build a pyramid ("Triangular 1-3-6" in my plot above).
But thanks for finding the official answer

I agree with you on that one m8
Its is only incorrect as much as only it is not the correct solution to the puzzle presented to us by the creator of this brainteaser.

☆

well not bad but does not really fit because in fact any one including even no one can go into a chat room and chat ... but there is a room that is a room but not any one or absolutely no one can enter it ...?

i think there are multiple answers
you just have to think about all the words that contain room somehow like broom or mushroom

not sure if thats genious... i was just thinking about the mushroom forest in subnautica a few moments ago

got it
A mushroom

I have to think about that theory again: