So, yesterday I found a kind of math quiz that I’d like to share with you. I’ll even give you the answer at the end…
Here goes: You and two of your friends on a trip decide to stay at a hotel. The clerk at the counter says a room costs $30 (nice and cheap!), so each of you pays $10, and you take your key.
After you go upstairs, the clerk realizes he made a mistake, and the cost of the room is only $25, so he gives five one-dollar bills to the bellboy, and asks him to run the money up to your room. On the way up, the bellboy realizes it’s going to be really hard to split $5 three ways, so he just pockets 2 of the dollars, and gives you all a total of $3, or $1 each.
So – if you each paid $10, and then got $1 back, that means you each paid $9, right? 9 x 3 = $27, plus the $2 the bellboy kept makes a total of $29, right? So where did the other dollar go?
For those of you who want to try to figure this out, I’ll distract everyone with a classic Ole and Lena joke from this part of the country. Ole and Lena are your stereotypical Norwegians – sort of. Here’s the joke:
Lena was really sick. She couldn’t even keep her lefse down. So, Ole calls for the ambulance to come and take her to the hospital. The dispatch person says, “So what street do you live on?” Ole says, “Chrysanthemum Street.” The dispatch person asks, “Can you spell that for me?” Ole says, “Ok – it’s C… uh Cr… no, that’s wrong… it’s…. Oh nuts – I’ll just drag her over to Elm Street.”
Have you solved the puzzle, or are you ready to hear the answer? If not, don’t read any more right now, until you are ready….
This puzzle is a prime example of trickery, as it invites you to go down the wrong path, mathematically. If sounds perfectly reasonable, except in terms of accounting, it uses the wrong numbers. It certainly does feel like everyone paid a net $9 times three plus the bellboy, and so $1 vanishes into thin air. But you see, we have jumped from one side of the ledger to the other. Let’s stay with the clerk, first of all. The room cost $30, and then only $25, so there was a $5 refund, right? Focus on the $5. Where did it go? $3 went to the three of you, and $2 went to the bellboy. So, $25 plus $3 plus $2 = $30.
Another way to look at it is to use simple algebra – you remember, when you had to keep things on either side of the “=” sign the same? So, we start with 10+10+10=30. Then we see that 10+10+10 = 25+2+3. Still with me? Ok, let’s take the money you got back out of the equation, which means 10+10+10 -3 = 25+2(bellboys money) +3 -3. You have to keep both sides equal, so you subtract 3 from each side. Or, you could even write it 10-1+10-1+10-1 = 25 +2.
So, now clean it up as much as you can, and you have 9+9+9=25+2. If you want to get rid of the bellboy’s money, then you take 9+9+9-2=25+2-2. Again, keep both sides equal. In two more steps, clean it up so that it’s 9+9+9-2=25. Then 9x3=27, so you have 27-2=25. Then of course, it’s 25=25. The final cost of the room, after you eliminate the five.
Another easy way is to say that you all spent a total of $27. $25 went to the room, and $2 went to the bellboy. Still $27 and not $29, since the $2 was already included in the total.
By now, I expect you have either gone on to see what today’s weather is, or you are regretting not paying attention in algebra class. Again, it’s all a matter of not getting distracted or walked down the wrong path in trying to solve a problem with the wrong information. Just as an aside – when I tried to tell the puzzle to Cheri, after she had already worked for 10 hours at the clinic, my brilliant partner STARTED with “Well, you spent $25 for the room…” Spoiled everything.
I share this with you as a fun example of how easy it is to get confused when we let someone else have control of the facts. Politicians of course are masters at this, as they replace one fact with a similar, but utterly wrong second fact, and then it’s off to the races with a flawed “spin” on the story.
The cautionary tale in all of this is what is true with every part of our lives. We must always listen intently, or intentionally. It’s not that we must live as skeptics, but we should always realize that any given fact is ours to accept or to question. We may choose to simply accept things with no filter or intentional thought – almost accidentally? But then, we must also accept the truth that very often, we may be led to a wrong conclusion, or at least a wrong beginning.
Always listen carefully – and in your mind, take time to ask the simple question: is what I have heard true? Is it factually accurate, and is it true in general, even if some of the facts are wrong? Or is it just plain wrong, like most rumors and second hand stories go?
90% of intelligence is discernment. I just made that up, but as I look at it, I believe it’s true. You don’t have to know all the facts about everything, since the great majority of what we are involved in is shaded and nuanced and an opinion. However, the ability to sort out the nuggets of truth from the pile of opinion is what will always determine a wise person, which I hope you and I can be named to be.
Enjoy all the puzzles of life. Just think things through.
Word for the day: linguipotent. Pronounced ling-GWIP-o-tunt. Another great Latin word, gathering up two smaller words, lingu meaning tongue, speech or language, and potens, meaning “power.” It is simply the mastery of a language, or the ability to involve interesting words to describe something. Another and even better word is logodaedalus. It’s Greek, with the first word, logos, which means “word.” Daedalus is from the name of the designer of the Minotaur’s labyrinth of Greek myth – it actually means “cunning worker.” So, if someone is logodaedalus, they are cunning and astute in their use of words. Whereas the first word seems to be fairly noble and aristocratic, the second word carries with it a sense of deceit or shady business. You can choose which you care to be!
After 43 years of ministry, Randy Cross lived his "fourth life" and shared about retirement, living boldly and intentionally in our world. To be sure, there was some North Dakota thrown in.