# Puzzle #29: Chocolate

Your sweetie loves chocolate. You bought your sweetie some chocolate: an assortment of 24 chocolates with six each of four flavours. “Oh, honey, you shouldn’t have.” Why not? Unfortunately, chocolate causes your sweetie to gain weight per the following table:

 Flavour Weight Gain in Pounds per Chocolate Eaten Nougat 1/4 Honey 1/2 Solid Chocolate 2 Emetic -1/4

Your sweetie selects four chocolates at random and eats them.

What is the probability of each of the following scenarios occurring (assuming no other factors that affect weight)?

• Scenario 1: Your sweetie gains five or more pounds.
• Scenario 2: Your sweetie’s weight does not change.
• Scenario 3: Your sweetie loses weight.

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, December 25, 2013 at noon Pacific Time. I will post the answer shortly after.

# Clear Communication

Is your communication good, close enough, or by guess and by golly?

In Odd Language #25: Appreciate or Not, I wrote of a bit of writing that said something that, while correct, was a bit more than I intended.

I have frequently run across writing that is unclear or that is ambiguous. Did the person really mean what got written, or was it close enough?

I wonder how many arguments have been started over this sort of carelessness. Or how many accidents have happened.

I hope you know what I mean. And I hope I know what you mean.

# Odd Language #25: Appreciate or Not

I recently posted to a technical listserve about a problem that I had been having for which I had managed to come up with a kludgy solution. I ended with: “I am glad that I found a solution, but I do not appreciate how awkward it is.”

The issue: “appreciate” can mean to feel positive toward or to understand. The sense intended above was the first, but remove the “not” and the second sense fits. I did not realise this subtext when I posted.

# Puzzle #28: Mystery Number

Consider the natural numbers from 1 to 200.

Consider the following properties that any one such number (n) may have:

• n is not even.
• n is prime.
• n is evenly divisible by 3.
• n is evenly divisible by 4.
• n is evenly divisible by 5.
• n is evenly divisible by 7.
• n is evenly divisible by 11.

Find the values for which the maximum number of the above properties is true. It need not be the same set of properties if there is more than one value.

(Hint: Do not use brute force. Consider how the properties interrelate. For example, if n is evenly divisible by 4, it can not be not even, and it can not be prime.)

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, December 18, 2013 at noon Pacific Time. I will post the answer shortly after.