You have some marbles each of one colour of red, orange, yellow, green, blue, and violet.
The number of red, yellow, and blue marbles are each even.
There are more red marbles than blue marbles, and there are more blue marbles than violet marbles.
The number of orange, green, and violet marbles are each odd.
The number of orange marbles plus the number of violet marbles is equal to the number of yellow marbles.
There are more marbles that are yellow than of any other colour.
There are at least two but no more than nine marbles of each colour. Each colour has a different number of marbles.
How many marbles are there of each colour?
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, October 26, 2016 at noon Pacific Time. I will post the answer shortly after.
My favourite month of the year is about to start. October having started, you might think that my favourite month of the year is November.
Actually, it is not.
My favourite month of the year is from about October 11 to November 10.
That is a one-month period.
If you were to ask ten people, “Which month is your favourite?”, all ten would probably give a calendar month answer. Why?
I am rather precise on the days, because the deciduous tree leaves are in full fall colours, and then, they start to fall. By the end of this month, the trees are fairly bare.1 This is not true of the calendar month October, nor is it true of the calendar month of November.
1Well, around here. If anyone from the southern hemisphere is reading this, yes, I know it is spring for you. I am discussing what I see. Do drop (push up?) a line though. I would be delighted to hear that someone Elsewhere follows my blog.2
2My first footnote on this blog.
I ran across an interesting post signature line recently: ‘”We must feed.” actually offering food.’
The issue: Some verbs can be tricky with two senses that could apply: one that is active and one that is passive. The usual sense of “We must feed.” is expressing being hungry, not that one must be a waiter. Another verb like this is “to photograph”. “I do not photograph well.” might mean that I am a camera klutz or that when I am photographed, the picture tends to not come out well.
Not long ago, the last ice cream truck of the season showed up. Each kid was determined to get there first to be sure to get his or her favourite treat this one last time.
Allison beat Bert there. Cindy beat Denise. Eric beat Frieda. Cindy was one or two places ahead of Frieda. Eric was three or four places ahead of Allison. There were no ties.
This is not enough to determine the exact order. There are still a number of possible orders. How many orders are possible given the above clues?
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, October 19, 2016 at noon Pacific Time. I will post the answer shortly after.