Category Archives: Puzzle

This category is for logic and math puzzles. Have some fun with logic and math. This is to put some fun into it.

Puzzle #229: Follow the Logic

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 <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, October 25, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #228: Frozen Yummy II

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 <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, October 18, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #227: Frozen Yummy

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.

How many ways are there to pay $4.20 with exact change using the usual Canadian coin denominations (nickel, dime, quarter, loonie, and toonie)? Wait; that would be boring. 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.]

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, October 11, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #226: What is the Rule?

If red is better than blue, starting better than quitting, something better than nothing, water better than wine, failure better than success, area better than volume, fast better than slow, and fast better than rapid, which is better: math or money? Why?

[Clue: The rule has to do with the spelling of the words.]

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, October 4, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #225: Textbooks

You are taking five courses, one each in Accounting, Biology, Computing Science, English, and Japanese.

The cost of the Japanese textbook is twice that of the English textbook. The cost of the Computing Science textbook is twice that of the Accounting textbook. It is also four-thirds of the cost of the Japanese textbook. The Chemistry textbook cost ten dollars more than the average cost of the other four textbooks.

If each textbook cost an exact number of dollars and you spent somewhere in the $300’s, how much did each textbook cost, and what is the total?

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, September 27, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #224: Fauxgo

Fauxgo is a language that I have just made up. (“faux” is French for false, and “go” is Japanese for language.) Fauxgo has three letters: A, B, and C. Words must be formed using certain rules:

An A can not immediately follow a pair of the same letter (eliminating “CCA”).
An A can not be immediately followed by a B (eliminating “CAB”).
A B must be doubled (eliminating “CBA”).
A C can not immediately follow a pair of the same letter (eliminating “BBC”) or follow two A’s that are at any point previous in the word (eliminating “ACAC”).
Three of the same letter in a row is not permitted (eliminating “AAA”).

Given these rules, what is the longest possible word in Fauxgo?

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, September 20, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #223: A Walk in the Park

You decide to go for a walk in Puzzle Park. The park is perfectly square and its sides run north-south and east-west. A path runs from the southeast corner to the northwest corner, and another path runs from the southwest corner to the northeast corner. The paths meet at the center of the park.

You start walking from the southeast corner along the path to the center. You walk one-half of the distance to the center. The joy of stomping on grass appeals to you, and you walk due north for the same distance. You then turn left and walk the same distance again and are back on the southeast-northwest path. You walk the same distance yet again toward the northwest corner. The grass-stomping urge overcomes you again, and you walk due south the same distance again, turn left, and walk the same distance for the last time.

At this point, you are somewhere in the middle of the park. If the park is 350 meters on a side, how far are you from the exact center of the park?

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, September 13, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #222: Statistics Abuse

Is it significant if 52.4% of cases meet a criterion?

Obviously, 524 cases out of 1000 would be 52.4%, but the numbers could be lower. They could be 262 out of 500 or even 131 out of 250. If you allow for rounding, it might be that a far lower number of cases meeting the criterion can be reported as 52.4%.

If you round to the nearest 0.1%, what is the lowest number of cases out of total cases that can be reported as 52.4%?

(52.4% seems so precise and “scientific”, but it is actually an abuse of statistics to report three digits of precision when one has fewer than 1000 cases total. This puzzle will show you how bad it can get; the numbers come from an article I read.)

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, September 6, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #221: Word Points

If answer is worth 16 points, cat 8, dog 8, Kamloops 19, puzzle 16, smoky 12, soap 8, yes 6, and yoyo 6, what is the rule for how many points a word is worth?

(Hint: The rule has to do with the letters, not the meaning of the word.)

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, August 30, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #220: Borders

How many Canadian provinces have exactly four straight lines for their land borders? For the purposes of this puzzle, a straight line is a line that runs on a line of latitude or of longitude and is primarily land. (Rivers and lakes are not considered to violate this, but a salt water coast does.)

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, August 23, 2017 at noon Pacific Time. I will post the answer shortly after.