Since it is that festive time of year, we have a fun little puzzle recommended to me by my aunt. Apparently, this is going around via an email chain, stumping people all over the country. Try and then come back here after—but only after—you have figured out the solution, which I provide below.
DO NOT LOOK BELOW THIS LINE!
You peeked, didn’t you? I knew that you would not be able to resist the overwhelming temptation to look below the line before you had worked out a solution. So I didn’t start the answer until later. My prescience is as great as Robin’s!
Now don’t you feel bad? Are you not filled with remorse (he said, deliberately echoing, yet at the same time mangling, a line from A Christmas Story)? Go back and work on it some more until you’ve got it or are truly stumped.
Actually, my purpose is to fill this space with meaningless chatter (I thought of pasting quotes from the New York Times) so that you can’t accidentally see the solution. La, la. How about them Lions? Did they actually win any games this year? I didn’t follow the NFL at all this year. This won’t interest you, but I stand in need of a haircut. I got a haircut once before while I was in Taiwan. Many great things about this country, but barbering Western style hair not one of them. When I removed myself from the barber’s chair, I found myself looking in the mirror at a gentleman who was the spitting image of Moe Howard. Yes, this turned out to be me. Thus, I will wait until I return Stateside before I am shorn.
That enough time wasting? On with the show!
HERE IS THE REAL LINE BELOW WHICH YOU SHOULD NOT PEEK
When most people are confronted with Robin’s regifting problem, they move quickly through it. If they give it any thought, they start with any number and figure the answer they arrive at by the computation can be any number. And that’s a lot of numbers! When the gift grid shows, they immediately hone in on their gift, usually without pausing to pay strict attention to the remainder of the gird.
Then, after locating the prize, they click “Next” and feel shock that Robin guessed correctly. Not content with the apparent psychic powers of a web site, people try again. Another match! What’s going on!
Any two-digit number can be written like this:
a * 10 + b
where a can be any number between 1 and 9, and b can be any number between 0 and 9 (a and b can be equal, of course).
The game asks you to pick a two-digit number and then subtract the first and second digits from it. That is equivalent to this:
answer = a * 10 + b – a – b = a * (10 – 1) = a*9.
Thus, the winning entries—the gifts—can only be at slots 9, 18, 27, …, 81, because a can be 1, 2, …, 9. To preserve symmetry, the game board prints all numbers from 1 to 99; however it is impossible for you to compute an answer larger than 81.
Next time you play, take a look at the gifts at those slots. THEY ARE ALL THE SAME GIFT. So no matter which number you pick, you will be lead to 9, 18, …, 81 and the gifts are always the same. Robin cannot lose.
Each time you play, the gifts are shuffled so that different ones appear at 9, 18, …, 81. Now, most of the numbers between 1 and 99 are, of course, impossible: the mathematical operation given in the rules will never let you deduce any numbers but those divisible by 9. But there are so many numbers displayed (99) that you will not see that many of the gifts repeat. Or if you did, you will tend to think that it does not matter. And gifts are not just repeated at the solution numbers, they are repeated for other numbers, too.
Make sense? Did you get it?
This ‘magic stunt’ comes around every year or so under another guise. More than one person has e-mailed one to me in perfect amazement that it worked.
As a member of, probably, the last generation that was taught to check calculations by ‘casting out nines,’ I think that it was easier for me to see through than those educated more recently.
Yes, the Lions have won. But they’ve also lost, and, on Nov 14, 2010, set a new record:
“Detroit Lions’ record 25th consecutive road loss comes against previously winless Bills” from: http://www.mlive.com/lions/index.ssf/2010/11/detroit_lions_lose_nfl-record.html (& other sites). This breaks their previous loss record set over 2001-2003.
Our home team has set yet another record….kinda makes one proud, in a way, eh?
On that date their record for 2010 was: 2-7 home & 0-5 away.
Amazingly since then they’ve not only won, they’ve won three-in-a-row!!! Making their record: 5-10 home & 2-6 away.
I suppose that’s a good thing — setting records in small increments rather than “quantum leaps” — so that they stay within reach for another record-breaking opportunity.
Puzzle obvious and trivial to any number geek.
However, the task of finding a decent haircut is extremely challenging. Warning: do not ask for the “senior discount”. The shops charge more to cut senior’s hair. I don’t know why. I have complained and complained but they offer no explanation.
essaress says.
‘casting out nines’.
Last generation indeed. It’s definitely not taught, even my children who attended Ivy Leagues schools think I am insane when I talk of the magic of ‘casting out nines’. They can never balance their checkbooks because they don’t know about the super secret way to find transposed digits.
Of course modern banks prefer that people not balance their checkbooks so they can invoke profitable, oh so profitable overdraft fees.
oh…. ummm… what is “casting out nines” does it have anything to do with gadarene swine? can someone illustrate for us numerically challenged folk–cheers brett
What’s a checkbook?
Ten points awarded for the use of “Gadarene swine”!!!
Well done, Brett.
PS — any attempt to compare global warming alarmists with the aforemention animals will result in the loss of points, so please control yourselves.
Ron does one lose points if we have above mentioned global warming alarmists say “we are legion” as they tumble over a cliff?–cheers brett
Too easy! The answer has to be that there’s something special about 10a+b-a-b, so you just see if there is.
Too easy!!!!!! Have a heart, sir. My mox was totally flummed.
Brett,
Of course. Calling them demon-possessed swine hell bent on mass suicide is a little over the top and will be frowned upon.
So, I get it.
I got as far as realizing the pultiples of 9 thing and the fact that 81 is the highest you can go, but I didn’t notice that the gifts on the grid changed because I didn’t go back to check again, so I though that she guess between 9 gifts depending on how long u took to make the calculation bc i was kinda set on the idea that it had something to do with time from the getgo. haha
tricky lol
Happy holidays!
She never guessed mine. I picked 28, then performed the prescribed calculation 11 – (1 – 1) = 11. She was way off.
kanny,
You have the wrong calculation. With 28, you should have come to the formula 28 – 2 – 8 = 18.
But if you had picked 11, you should have come to 11 – 1 – 1 = 9. This is not the same as 11 – (1 – 1) = 11 – 1 + 1 = 11.
There were two cannibals dining on a clown. One turns to the other and says “Does this taste funny to you?”
( I was playing on the slight ambiguity in the instructions for fun ). Oh well.