Trick of Mind

A deck of cards is split into 4 piles of 13. You take 1 card at a time from the top of any of the piles. Repeat until there are no cards left. How many different orders could you do that in?

If you crack that, then you should be able to generalise to piles of different sizes, etc.

To be clear, initially there are 4 choices at each step. That remains the case until you empty a pile, and then you’ll only have 3 choices at each step, etc.

Seven gents A,B,C,D,E,F and G play a silly game. In order of their names, each doubles the amount of money that the others have in their pockets (from his own pocket). i.e. the money simply gets redistributed.

When all seven have taken their turn, each ends up with $128.

How much money did each of the gents start out with?

This is like another old ToM. LOL and pretty easy.

If each of the “+”’s could be either “+” or “-” or “*” or “/” then
how many different answers could there be?

And what would be the largest and the smallest answers?

Here’s one I pinched from the old ToM site. In my opinion, the official answer was wrong and only one person got it right (for the right reason). I’ll post a link to the page after this has run it’s course.

Tom, Dick and Harry are in prison. One of them has been randomly selected to die in the morning, and the other two will be set free. Their guard knows which one will die, but none of the prisoners does. The guard is under strict instructions not to divulge the identity of the doomed man.

Tom is desperate for any information beyond the fact that his probability of death is one in three. He begs the guard to throw him an informational bone. Finally, to shut him up, the guard agrees to reveal only the following: the name of one of Tom’s fellow prisoners who will be set free rather than killed. The guard then says that Dick will be set free.

After receiving this information from the guard, what is the most accurate calculation Tom can make of the probability that he is the doomed man?

A group of 10 people are seated at a circular table. They hadn’t noticed that they had places designated for them, and none of them sat in the right place. If the table is rotated by one position, calculate the probability that 0,1,2,3,4,5,6,7,8,9,10 of the people are then seated at their correct position. Similarly, calculate the probabilities if the table is rotated (in the same direction) one more position, etc.

This problem was inspired by Ragknot. I haven’t thought about it much, my initial belief is that it’s fairly easy, but I could be wrong. If I’m right about it being fairly easy, then it should also be the case that you can give a general solution, rather than loads of numbers.

For consistency in the solutions, consider that the names of the people are “1″,”2″,…”10″, and that the seats are labelled in the order 1,2,3,…,10 (like a clock that only has 10 hours on it’s dial). The clock/table is only rotated (one place) anti-clockwise, so that someone who started in seat n will be in seat n+1 (mod 10).

In case you don’t know where to start, this problem is all about derangements

Six logicians finish dinner. The waitress asks, “Do you all want coffee?”

First logician: “I don’t know.”

Second logician: “I don’t know.”

Third logician: “I don’t know.”

Fourth logician: “I don’t know.”

Fifth logician: “I don’t know.”

Sixth logician: “No.”

Who gets coffee and why?

1) My uncle on my mom’s side is an only child. Explain.
2) A man who runs in front of a car gets _____. A man who runs behind a car gets _____.
3) Everyday at a company of 100 people there are 99 vehicles in the parking lot. Each employee leaves their house in the vehicle they own. How is this possible?
4) If the sky is yellow and a banana is red, then what color is grass?
5) Is it legal to marry your Great-aunt’s only sibling’s granddaughter’s only cousin?
6) 1 + 1 = ? (hint: not 2)

A young lady got lost in a museum. There is a 80% chance that she is in the dinosaur section, and a 20% chance that she is in the aquarium section. Six people are available to search for her. Each searcher has a 20% chance of finding her. If you can only do one search, what is the optimum way to split the six searchers up? e.g four searchers to the dinosaur section and two to the aquarium section.

This was said to be a complex estimation of how much water will seep out of a reservoir. One thing you should understand is the top surface area is given, but the seepage comes from the surface of the ground under the water. For a specific reservoir, a table can help you estimate the seepage. I will give you brief table and what the seepage would be for a specific volume. If you can understand how it was computed,  I’ll ask you to give the seepage for a different volume.

When the reservoir surface is 38 acres, the seepage is 0.9 inches.
And if the reservoir is 71 acres, the seepage is 1.4 inches.
And when the reservoir is 209 acres, the seepage is 2.1 inches.

Ok… here’s one solution…

When the surface of the reservoir is 77.18 Acres

When the surface of the reservoir is 200 acres ,
what will be the seepage in Acre Feet?

Oh,  this is an additional item.   This is seepage for a month.  The surface is measured at the first of the month and at the end of the month, seepage gave surface level went down in the given inches.

This a specific part of the USA’s National RESOP program written in Fortran in 1987.

A group of 10 people are seated at a circular table. They hadn’t noticed that they had places designated for them, and none of them sat in the right place. Prove that simply by rotating the table, that at least 2 of them can be sat in the right place.