Monthly Archives: January 2014

Puzzle #32 Solution: Backgammon Dice

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Puzzle #34: Good Bets?

You are at a carnival. One of the midway games involves flipping three coins each marked with a 2 on one side and a 3 on the other. You pays your money, and you takes your chances. Each coin is flipped randomly. In each game, you win the product of the face-up numbers on the flipped coins in dollars.

In the first game, you pay $16, and you are paid as above.

In the second game, you pay $20, but there are two sets of flips, and you get paid according to the better set of flips.

In the third game, you pay $12, but there are two sets of flips, and you get paid according to the worse set of flips.

On average, what can you expect to win/lose in each of these games? Which of the three games is the best to bet on, and would you bet on it?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 29, 2014 at noon Pacific Time. I will post the answer shortly after.

How Old Is the Shepherd?

“There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”

What you do think the answer is?

“How Old Is the Shepherd?” is the title of an interesting article on math. There are various versions on the Web; one is at <a href=”http://blogs.law.harvard.edu/reyes/files/2006/05/ShepMersth.pdf”>http://blogs.law.harvard.edu/reyes/files/2006/05/ShepMersth.pdf</a>.

Take a look at the article to see how well children faced with this problem did. How well did you do?

Just because there are numbers does not mean that they go together.

Puzzle #33: Pawns

In chess, pawns start on the second row away from a player and proceed toward the eighth row.  Each pawn starts on a different column.  Pawns move forward one space (or two on the first move, if desired) and capture diagonally forward.  Some spaces can be reached by only some of the eight pawns.  How many of the 64 spaces can be reached somehow by all eight pawns?

Submit your answer to Gene Wirchenko &lt;genew@telus.net&gt;. Your answer should be in the form of a proof. That means to show how your answer must be correct. <strong>The deadline is Wednesday, January 21, 2014 at noon Pacific Time.</strong> I will post the answer shortly after.

Puzzle #31 Solution: More Chocolate

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The Solution That Becomes a Problem

There is an old saying: “Perfection is the enemy of the good.” There should be one that the latest version is the enemy of the good.

I use Windows XP on my main computer. I am happy with it. I have two computers on my desk. One is my XP system, and the other is a Windows 7 system. In their less than infinite wisdom, Microsoft does not let 16-bit programs run on 64-bit Windows 7 without you installing a special program (XP Mode) and that program will not run on some versions of Windows 7 (like the one on my laptop).

I have a number of 16-bit utilities that I wrote. I am not keen to rewrite them. Consequently, I have not switched over to Windows 7.

Why switch to the latest version when it will break something?

Guess what? After my experience with Windows 7, I saw no real need to even think of trying Windows 8.

Since switching versions will cause problems, why bother?

Computers can be great for solving problems, or they can create problems. I much prefer the former, and I will go to some lengths to stay in that category. How about you?

Puzzle #32: Backgammon Dice Rolls

Rolling two six-sided dice gives an average roll of 7.

In backgammon, doubles count for double the usual roll. For example, double 4 is worth a count of 16.

What is the average roll under backgammon rules? What is the probability of a roll being over the average?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 15, 2014 at noon Pacific Time. I will post the answer shortly after.

Puzzle #30 Solution: The Zillion Bracelet

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