Can you tell me some unsolved mathematical problems?

The Millenium Prize problems. Solve any one of 'em and get a million bucks.

3 Travellers share the cost of a $30 hotel room. They each pay 1/3 rate of $10 per person. After check-in the manager noticed a $5.00 rate reduction was overlooked by the front desk. To correct this he sends the Bellman over with the refund. The happy travellers give a $2.00 tip to the Bellman, then split the remaining $3.00 equally. The problem is whether you add or multiply there is no way to account for all $30.00 used in this problem. 9 x 3 = 27 plus 2 = 29. Sorry folks that dollar is gone forever. I have made my own addition to this problem to stump us even further. At the end of the month the company over reimbursed the travellers for this expense by $2.00. But they oare ok with it because they too can prove they are correct. The company records justify the reimbursement of $29 as follows. $9 paid each x 3 = 27 plus 2 tip = 29, however the re-imbursement should only be $27 because $30 original paid - $5.00 refund = $25 plus $2.00 tip equalls $27 not $29. I doubt they will every know it because they have mathematical proof that shows they made no mistake.

For the $10 a room question....the $1 is accountable if you go backwards. Original price of room: $30 or $10 ea per person. Discounted price of room was $25, or $8.33 per person...NOT $9.00. Makes sense?

Solve this out:

Madhulika and Rita ran a 2km. race twice. Rita completed the first round 2 min. earlier than Madhulika. In the second round Madhulika increased her speed by 2 km/hour and Rita decreased her speed by 2 km/hour. Madhulika finished 2 min. earlier than Rita. Find their speeds of Running the first round?

if u can divide any angle into 3 equal angles without using tales theory, someone asked me abou this and to devide any side into 3 equal sides i have created a new theory how to devide the side into 3 equal parts but till now couldnt devidethe angles

calculating PI to its termination and or repeting point. they have been trying to do that one for thousands of years