Welcome to The Puzzler. Every week, there are 2 new puzzles related to my passion: math, logic, and thinking. The first puzzle will be The Puzzler Quik, meant for those who crave something fun-sized. The second puzzle will be The Puzzler Think, meant for those who love to ponder. The answers will be posted in next week’s column. Don’t forget to submit your answer for a potential shout-out in the next edition of the Puzzler.
Puzzler Quik
The 2021 AMC 10 had 25 multiple choice questions. If each correct question is worth 6 points, incorrect questions are worth 0 points, and questions left blank are worth 1.5 points. What is your score if you get 22 questions correct, 1 incorrect, and leave 2 questions blank.
Puzzled?
Multiply the # of correct questions by 6, and the blank by 1.5 and then add your total!
Your correct questions are worth 132 and incorrect questions are worth 3.
Add these up to get your answer.
I have a calculator that can display ten digits. How many different ten-digit numbers can I type using just the 0-9 keys once each, and moving from one keypress to the next using the knight’s move in chess? (In chess, the knight move in an L-shape – one square up and two across, two squares down and one across, two squares up and one across, and other like combinations)
Puzzled?
What digit must you start with?
The answer is not very big, and a bit of casework should suffice!
ANSWERS TO LAST WEEK’S PUZZLERS
Last Week's Puzzler Quik
Eddie From New York was the winner of this shout-out!
To increase 12 by 25%, we multiply it by 5/4(why?): $$12\cdot\frac{5}{4=15}$$ So, your new score would be 15!
Last Week's Puzzler Think
The shoutout for this problem goes to Pranav from New Jersey!
We can disregard all the digits except the last one. So, this is the same as \(2^{20000}\). The powers of 2 follow a pattern in the unit digit. It goes like this: 2, 4, 8, 6, 2, 4, 8, 6 etc… Since each power that is a multiple of 4(and 20,000 is a multiple of 4) ends in 6, our answer is 6.
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