Start with the number 7. Then follow these steps in order.
Step 1: If it is true that arutta, then add 5; if not, add 7.
Step 2: If it is true that budrist, then multiply by 2; if not, multiply by 3.
Step 3: Subtract twice the number you added two steps ago.
Step 4: Divide by two.
Your answer is a two-digit prime. Is arutta true, and is budrist true?
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 25, 2017 at noon Pacific Time. I will post the answer shortly after.
“It doesn’t matter who you vote for, the government always gets in.”—Unknown
Well, the results of the by-elections I wrote about last week are in. The candidates I voted for did fairly well relatively speaking.
I voted for Bill McQuarrie for mayor. He placed second with 2,661 votes (18.34% of the votes). The winner was Ken Christian with 9,274 votes (63.91% of the votes). The other candidates all got fewer than 1,000 votes each.
I voted for Ray Dhaliwal and Bill Sarai for councillors. The winners were Kathy Sinclair with 3,421 votes (12.29% of the votes) and Ray Dhaliwal with 3,292 votes (11.83% of the votes). Bill Sarai placed fifth with 2,182 votes (7.84% of the votes). If the percentages look low, remember that there were 21 candidates for two positions. There was no big gap as in the mayoral race; the numbers just gradually become less as you go down the list.
With the number of candidates, I wonder how badly the vote got split. Over time, first past the post voting tends to reduce the number of candidates to two. For an excellent explanation of this, watch
The Problems with First Past the Post Voting Explained by C.G.P. Grey. He also has other videos on other voting systems (and other subjects, too).
(The election results come from Kamloops This Week which is Kamloops’s newspaper.)
The issue: I thought this about a confusion at work that I had worked out. My boss’s assistant might have asked, and that is how I could have replied. However, my job involving preparing rock and soil samples for processing; this is called sorting. This means that when I had the confusion sorted, I did not have the work (sorting) done. I would have created another confusion. Context counts!
The yummy, chocolate-coated, ice cream thing on a stick that you – OK, OK, I – have been buying costs $4.20 at the local store near where I work. No, I forgot about the tax; it costs $4.45.
How many ways are there to pay $4.45 with exact change using the usual Canadian coin denominations (nickel, dime, quarter, loonie, and toonie)? Avoiding boredom once again, how many combinations consist of six or fewer coins?
[Hint: You can save yourself some effort if you look at the problem in the right way. Is this the same way as in the previous problem?]
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 18, 2017 at noon Pacific Time. I will post the answer shortly after.