Sandwich-making rules: A sandwich has one or more layers of ingredients. You have five ingredients: three jams (raspberry, blueberry, and blackberry) and two nut butters (peanut and almond). You can use an ingredient only once in a sandwich. Two jams can not be adjacent layers; two nut butters can not be adjacent layers. Two sandwiches with the same ingredients arranged top-to-bottom and bottom-to-top are the same type, but if the order is otherwise different, they are different types. (Sniff! It is something about being a gourmet.)
How many distinct types of sandwiches can you make?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, May 25, 2016 at noon Pacific Time. I will post the answer shortly after.
Not too long ago, I got a new wristwatch. While it looked good, it had a nasty flaw. It had very little protection against water. A quick rinse to get rid of accumulated sweat would end up with water under the plastic. After a few of these, some of the water got into the electronics and some of the LED segments quit working.
Had I known that this watch was so vulnerable, I never would have bought it since I regularly rinse my watch.
The trouble with cheap designs is that the corners cut are often not mentioned. You proceed with normal use and break it. Consider spending a bit more, you cheapskate. (Who? Me?) I just did for another not-quite-so-cheap watch that is marked “Water Resistant”. Here is hoping.
Recently, an author posted the following to the USENET newsgroup rec.art.sf-written: “I was born within 20 miles of where my wife was born, but our parents were born scattered over four states, …”
The issue: He corrected this later: ‘Onbviously[sic], I meant, “Our parents’ birthplaces were scattered among four states.”‘ Misplaced modifiers are a common, writing error.
You have some marbles, each of one colour of red, orange, yellow, green, blue, and violet. You have one of one colour, two of another colour, and so on up to six of one colour. There are fewer red than green marbles. The number of orange marbles divides evenly into both the number of red marbles and the number of blue marbles. The number of yellow marbles divides evenly into the number of blue marbles. Each of the numbers of orange, green, and violet marbles is prime.
How many marbles are there of each colour?
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, May 18, 2016 at noon Pacific Time. I will post the answer shortly after.