Contest #2 deadline is being extended, and a hint! Also, everyone who entered Contest #1 WON!
First of all, as I said in an earlier blog, the response to the first contest in Paul’s Puzzle Page was UNDERwhelming, SO… everyone who entered, regardless of how many of the 26 clues they got right (I said you didn’t have to get them all!) won $25 worth of 3/4″ Green-tagged items of their choice!!! Congratulations!
Now, on to the current contest (#2) - the FOUR TWO’s Puzzle. Originally, the deadline was this coming Sunday, 9/23. I’m extending it to Wednesday, 9/26. So far, I have received only ONE entry and the contestant probably felt like he found all 20. Unfortunately, I have some issues with two of the expressions. They both involve the use of “(arcsin(inv(2))”. For those not mathemathically inclined, skip the rest and just remember - you only NEED an algebra I background, and here’s a big hint: no one said you couldn’t use “.2″, as in two-tenths!! Ah, a light goes on!!
Now back to the problems with the entry: The submission has (arcsin(inv(2)) - 2) / (2+2) to represent the number 7. I understand the intent, but it is not a valid mathematical expression for the number 7!
1) “inv” is not to my knowledge a recognized symbol for a math operation. I’ve never seen it used in a math problem and a “google” search of math symbols yields no results. I assume it was meant as an instuction to find the “inverse” of 2, more specifically the multiplicative inverse or reciprical (1/2), not the additive inverse of 2 (-2). Yes, graphics calculators may use the abbreviation of “inv” to indicate the notation that one is going to find the “negative one” power of the entry, but it is not written with this shorthand in an expression - only in an instruction manual of how to make entries with the calculator.
2) Let’s suppose we forget that problem and focus on what would now be “arcsin(1/2)”. Again, I have to assume that the user is using degrees and not another form of measurement such as radians. It should be stated, but let’s ignore that. When “arcsin” is introduced in trig, it is used to indicate those angles that have a value of “1/2″ for their sine, namely 30 degrees (Pi/6 radians) or 150 degrees (5Pi/6 radians) or any of an infinite number of angles coterminal with them, such as 390 degrees, 510 degrees, and so on. To narrow the field to a specific one, namely the closest angle to zero degrees, it should be noted as Arcsin - use a capital letter. Granted, even among “professional” mathematicians, this distinction is sometimes ignored. So, let’s ignore this problem, also, which leaves us to a major one…
3) Assuming that we have allowed everything to go so far and are using degrees, what angle closest to zero degrees has a value for its sine equal to 1/2? 30, right? NO, 30 DEGREES!! 30 has a label, a unit, and it is important and significant. It does not represent the concept of a quantity, such as 30, but a portion of a sweep with respect to a circle. The circle can be of any size. As we all remember from school, you can not add or subtract terms unless they have the same unit/label. So, how can we take “2″ from “30 degrees”? Answer: it can’t be done!
I know it looks and sounds like nitpicking, but it is a crucial part of math!
In all fairness to the entrant, I will allow him (Robert, you know who you are!) to submit new expressions for your “7″ and “17″ tries.
September 23rd, 2007 at 2:39 am
Can we have a contest like “Guess the celebrity cleavage?” I would maybe have a chance then……