Add another pill from container A. Now you have 4 pills. Divide each into 2 parts, keeping them separate from the others. Now take one half from each group. You will have one A and one B. Take the rest of the halves the next day. And from then on - BE CAREFUL!!!

The whole fish is $10/kg

So, you lose $7/kg on the Head when you sell at $3/kg

You lose $3/kg on the body when you sell at $7/kg

So, you lose $7x5 + $3x5 = $50 when you sell it by halves.

envelope

$262, $252, $289, $233, $315, $229, $403, $208, $487, $198

giving a total discount of $707.61 with rounding of the final prices but not the discounts.

Absolutely correct preflop (#2)- gramps (#4) gives a nice explanation. So, I don't have to add anything!

Here's an easy one and may have been posted earlier but I couldn't find it...

The other day our local club organized a knock-out tennis tournament. Unfortunately, there were only 29 players who signed up. If there were 3 more players, everything would have been so much easier! But now, the organizers had to figure out 1st round "bye"s and, if necessary, "bye"s for other rounds as well. Well they did take care of it ultimately. Considering all these "bye"s and what not, how many matches were played?

There is a regular way of figuring this out and an easy way. I'm more interested in the easy solution.

Ghosts are very real....they are human spirits....and human spirits are not always visualised.....it is all emotionally connected......like when you feel happy or sad or cranky, etc....you can only sense them emotionally....the physical viewing of ghosts comes after that.....if they choose......

I am from the other end. I think that the feeling of the presence of ghosts or any other spirits, for that matter, is not real! But who is to say that I am correct in my belief?

6x9 = 54 in the decimal system corresponds to 42 in a number system with BASE 13!

The binary process is the best one for problems of these types. But it works with one weighing only if the weight of the counterfeit coins is known. Since this is not the case, the second weighing is necessary!

I meant, ( angular speed ),

As far as I remember, angular velocity and angular speed are essentially the same thing. Angular velocity, in the strict sense, is a vector where the direction of the vector is the axis of rotation. But for our purposes, they should be treated the same.

If by "speed" we mean "angular velocity" then all planets will take the same time to rotate about their axis. The "day" will be the same and hence the "year". All of the babies would be 15 years old.

If, however, we are talking about "linear speed" or "surface velocity": the smaller planet would then rotate twice as fast and the larger planet half as fast. So, in the same amount of time (15 Earth years), the smaller planet will have twice the number of days, hence twice the number of years. So the age of the baby will be 30 years. Similarly, for the bigger planet, the age would be 7.5 years.

I guess the problem boils down to a simple definition. By "speed" do we mean "linear speed" or "angular velocity"?

I ask person A the following question:

"If I were to ask you whether Person B is a 'Truthteller', would you say Yes?"

If A is a TT and B is a TT: Answer Yes

If A is a RS and B is a TT: Answer Yes

If A is a TT and B is a RS: Answer No

If A is a RS and B is a RS: Answer No

So, is the answer is Yes, you choose B.

If you are unlucky, you may have to repeat this for maximum six times to get your man.

You've got it! 4,000 is correct and, I might add, you gave a very simple explanation.

From the info given, we can get the following Truth Table:

Truth Lie

75% 7500 5625 1875

10% 1000 0000 1000

10% 1000 0250 0750

05% 0500 0000 0500

# 10000 6875 3125

So, 68.75% of the students will say the truth while the rest will lie.

Given that 4,625 students said YES, 68.75% of that number, that is 3,180 students actually did.

Out of the rest of the students (who said NO), 31.25% would be lying, that is 1,680 would actually have.

In total 4,860 students are likely to have experimented with illegal drugs.

You guys are awesome!!! I really enjoyed the exchange of ideas including the cocky ones.

The 2 key factors here are:

1. The lion is 4 times faster than you

2. He anticipates your every move with a zero response time, which means he will be at the spot you are most likely to cross the circle

Also, do remember that while the lion can run 4 times faster than you, he doesn’t necessarily have to. He will always try to anticipate your move.

Regarding k-man’s solution (#3):

While the spiral trajectory seems the most elegant mathematical solution, I am not too sure that it would work with the 2 points stated above. I think (don’t have a formal proof yet), as you approach the edge of the circle, the lion would be able to keep up with you with his faster speed. K-man, please correct me if my logic is in error.

Solution:

If you run along a circle of radius 0.25, the lion would be just able to keep up with you (at 4 times the speed). If you are slightly inside that circle (radius just less than 0.25), you will be able to gain on the lion. You keep running along that circle until the lion is diametrically opposite to you. Then head straight for the edge. You will have to run slightly more than 0.75 units while the lion has to cover pi!

Imhere (#8) was on the right track, but his numbers were a bit off!

You are standing in front of a L-shaped trench. The trench is 5m wide, very deep and continues as far as you can see in both directions. All you found lying around are 2 boards that are strong enough to support your weight, but unfortunately they are both just a bit shorter than 5m. You have no rope, screws, nails or any other way to securely connect the two boards together. All you have are these 2 boards. How do you cross to the other side of the trench?

How do you attach a drawing so that it is hidden (like a spoiler)? Being a Newbie, I didn't realize that the attachment would show.

Place the 2 boards at the corner of the trench as in attachment.

My mistake. The lion's speed is 4 times yours - not twice, as originally stated. Sorry for the confusion!

You are at the center of a unit circle (radius=1). A hungry lion is on the circumference and for reasons unknown can only run on the edge of the circle. He is, however, twice as fast as you are and his reflexes are instant (response time=0). So, in whichever direction you start to run, he will instantly run towards that spot on the circle that you are most likely to cross. Is there any way you can escape? (To keep things simple, please consider the lion and yourself as point entities!)

All squares (1, 4, 9, 16,...) will be open. All others will be closed.

It's strange but true that a cork will not stay in the center of a glass of water. Instead it will slowly drift over to the side of the glass, where it will remain. There is, however, a simple way to make the cork remain floating in the center of the glass.

(Swirling the water is not the answer.)

Fill the glass nearly to the top and place the cork. Now add just a little more water so that the water forms a convex shape without overflowing. The cork will seek the highest point which is the center of the glass.

a=0, b=3, d=5, e=6, g=4, i=2, l=9, o=7, r=1, s=8