2 Eggs and A Building

[Hàkon]

I can give you a message.
Is that fine instead of a massage?

All is welcomed.

[Hàkon]

Well, since Osprey has not provided a new nut to crack I have come up with my own:


I have three coins in my pocket that I, with huge precision, fit into the smallest equilateral triangle conceivable.

All three coins fit exactly, and sit as close next to each other as possible.

How great is the percentage of the triangle's area which is not covered by the coins?

[el22]

If I've understood it right (and haven't done any errors) the solution should go:
r = coin radius
Triangle area = r*r*(tan(30)*4 + 6)
coin area = 3*pi*r*r
no calculator to calculate the actual value

[Osprey]

Well, since Osprey has not provided a new nut to crack I have come up with my own:


I have three coins in my pocket that I, with huge precision, fit into the smallest equilateral triangle conceivable.

All three coins fit exactly, and sit as close next to each other as possible.

How great is the percentage of the triangle's area which is not covered by the coins?

Sorry, couldn't get any puzzle which might puzzle you
The answer is 16.something percent, if i have my calculations right.
Here's another one. (pretty simple)
I have 100 coins on the table. Out of them exactly 50 are heads up. You are blindfolded. You have to seperate the coins into two stacks with equal number of heads up. And you can't feel the coins. (assume a paper covers each side of the coin)

[Quasimodem]

Well, since Osprey has not provided a new nut to crack I have come up with my own:


I have three coins in my pocket that I, with huge precision, fit into the smallest equilateral triangle conceivable.

All three coins fit exactly, and sit as close next to each other as possible.

How great is the percentage of the triangle's area which is not covered by the coins?

Okay, is it 21.46%?

[Osprey]

Is it...

????

What a cute, childlike handwriting?!!

[el22]

I've done an error earlier on, tan(30) should be 1/tan(30) and if everything else is OK the answer should be 39%

[el22]

Sorry, couldn't get any puzzle which might puzzle you
The answer is 16.something percent, if i have my calculations right.
Here's another one. (pretty simple)
I have 100 coins on the table. Out of them exactly 50 are heads up. You are blindfolded. You have to seperate the coins into two stacks with equal number of heads up. And you can't feel the coins. (assume a paper covers each side of the coin)

My brother told me about a trick with cards he had seen in youtube, similar to this problem. So the solution should be:
1. divide the coins in two groups with equal number of coins
2. turn over the coins of one group

[Quasimodem]

What a cute, childlike handwriting?!!

Well, it's a true Microsoft Paint Masterpiece. Art at its finest. But now I'm getting 21.46%...

[Hàkon]

I've done an error earlier on, tan(30) should be 1/tan(30) and if everything else is OK the answer should be 39%

What a cute, childlike handwriting?!!

Okay, is it 21.46%?

All wrong.

Also, I would like to see your full calculations.

Would you like to continue guessing or do you perhaps want the answer?