bonanova Posted August 17, 2008 Report Share Posted August 17, 2008 It goes like this, said Alex, you write down a three-digit number. Davey tried to stifle his yawn, but couldn't. Ian's eyes were glued to the blond at the bar, and Jamie had fallen asleep. It was next to closing time at Morty's, and even Alex wasn't getting much attention. Then I'll tack on three more digits before you can take a gulp of yer ale, and I bet that the resulting six-digit number will be divisible by 37! I don't think so, said Ian, as the blond strolled off to the ladies room. Not even you ... Well, I'll show you, interrupted Alex, and this one is for free. Give it a try. Ian quickly scribbled 412 on his napkin and reached for his mug. But before he could lift it, Alex had written 143 at the end, and quick-witted Davey verified that 412,143 was in fact equal to 11139 x 37! And that's not the half of it, boys, Alex was finding his groove now, I'll do the same thing only this time I'll add on six digits to yer number! Again, Ian obliged, this time writing 341. It took Alex only a second to make that into 341,203,122, and Davey's pocket calculator verified that dividing by 37 gives an even 9,221,706! Well I know now you'll never take my bet, continued Alex, so I'll make you an easier one. Clearly I don't do math that quickly, so we all know there's trick involved. So here's what I'll do. You give me ten numbers, and I'll add three digits, or six digits, before, after, or some of each to all ten numbers. Looking at what I've done ought to lead you to figure out the trick. If you do that, I'll buy one round before closing. Ya don't get an offer like that one every day. That woke Jamie up, and along with the others, they wrote down the following ten numbers, and Alex added the digits in red. Davie verified the results. It took Jamie only a moment. I have it! What did Jamie see?253,413 = 37x6,849114,762,012 = 37x3,101,676620,379 = 37x16,767247,340,412 = 37x6,684,876458,541 = 37x 12,393275,613 = 37x7,449123,141,513 = 37x3,328,149201,471,216 = 37x5,445,168302,364 = 37x8172121,235,310 =37x3,276,630 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 37 goes evenly into 111. If you add each adjacent 3 digit number within the 6 or 9 digit number together you will find that the resulting 3 digit number is divisible by 111. This is a property of divisibility by a number made up of only 1's. It also works for 2-4-6 etc. digit numbers with 11. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 37 goes evenly into 111. If you add each adjacent 3 digit number within the 6 or 9 digit number together you will find that the resulting 3 digit number is divisible by 111. This is a property of divisibility by a number made up of only 1's. It also works for 2-4-6 etc. digit numbers with 11. Dammnn clueless!' I wil have to pay more attention to you in mafia! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 Dammnn clueless!' I wil have to pay more attention to you in mafia! Especially after the that just went down with Mekal and the Spy! Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 17, 2008 Author Report Share Posted August 17, 2008 Alex slides a cold one down the bar to clueless. Quote Link to comment Share on other sites More sharing options...
0 Prime Posted August 17, 2008 Report Share Posted August 17, 2008 Why alcohol is the driving force behind mathematical discovery at Morty's? Patrons remain largely indifferent to Alex's challenges, until he offers to buy drinks. Can we implement something similar at this forum? Alex, probably, takes advantage of the fact that both 1000 and 1,000,000 yield remainder 1 wheh divided by 37. Since Alex's abilities to perform fast calculations are not so great, he must be using the number 111, which is divisible by 37. And, therefore, 222, 333, 444, ... and so on. For example, since 1000 mod 37 = 1, then 412,000 mod 37 = 412. Alex has to find what to add to 412 to make it divisible by 37. Since he knows 444 is divisible by 37, he is probably capable of finding that 412 + 32 = 444. To camouflage it further, he adds another 111 to it. Thus 412,000 + 32 + 111 = 412,143. The calculations, even Alex can perform in his head. Similar method can be used with millions. The orginal number plus number of millions plus number of thousands plus the number represented by the last 3 digits is the remainder from the division by 37. For example, 123+141+513=777. So starting with 513, Alex has to find two more numbers wich will add up together with 513 to 666, or 777, or 888 and so on. That reminds me of some tricks I saw many years ago in Martin Gardner's books. Those tricks were based on 7*11*13=1001. And any 3-digit number multiplied by 1001 is that number written twice. Bonanova, I'm curious: is Morty's bar your own creation? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 18, 2008 Author Report Share Posted August 18, 2008 Why alcohol is the driving force behind mathematical discovery at Morty's? Patrons remain largely indifferent to Alex's challenges, until he offers to buy drinks. Can we implement something similar at this forum? I certainly hope so ... Quote Link to comment Share on other sites More sharing options...
Question
bonanova
It goes like this, said Alex, you write down a three-digit number.
Davey tried to stifle his yawn, but couldn't. Ian's eyes were glued
to the blond at the bar, and Jamie had fallen asleep. It was next
to closing time at Morty's, and even Alex wasn't getting much attention.
Then I'll tack on three more digits before you can take a gulp of
yer ale, and I bet that the resulting six-digit number will be divisible
by 37!
I don't think so, said Ian, as the blond strolled off to the ladies
room. Not even you ... Well, I'll show you, interrupted Alex,
and this one is for free. Give it a try.
Ian quickly scribbled 412 on his napkin and reached for his mug.
But before he could lift it, Alex had written 143 at the end, and
quick-witted Davey verified that 412,143 was in fact equal to
11139 x 37!
And that's not the half of it, boys, Alex was finding his groove
now, I'll do the same thing only this time I'll add on six digits to
yer number! Again, Ian obliged, this time writing 341. It took
Alex only a second to make that into 341,203,122, and Davey's
pocket calculator verified that dividing by 37 gives an even 9,221,706!
Well I know now you'll never take my bet, continued Alex, so
I'll make you an easier one. Clearly I don't do math that quickly,
so we all know there's trick involved. So here's what I'll do.
You give me ten numbers, and I'll add three digits, or six digits,
before, after, or some of each to all ten numbers. Looking at
what I've done ought to lead you to figure out the trick. If you
do that, I'll buy one round before closing. Ya don't get an offer like
that one every day.
That woke Jamie up, and along with the others, they wrote down
the following ten numbers, and Alex added the digits in red.
Davie verified the results.
It took Jamie only a moment. I have it!
What did Jamie see?
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