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October’s Puzzle: Two Mathematicians
Two mathematicians (let’s call them M and N)—once good friends—meet after a long time to have a drink together. M asks, “Are you married? Any kids? Do you still live in that old apartment building?” N replies, “Yes, I'm married with three kids, and we live in a private house now.” M asks, “How old are your kids?” N replies, “Let me answer with a riddle: The product of the ages of my kids is 36. Now, see that bus over there? The sum of my kids' ages is equal to that bus number.” M thinks for a moment, then says, “I don’t have sufficient information to solve the puzzle.” N replies, “Oh, yes, you’re right, I forgot to mention that one of my kids was born before we bought the house.” Soon after N provides this last bit of information, M solved the puzzle and told N the correct ages of the kids. Can you figure out the solution? Also, how would the solution change if N’s additional piece of information was that one of his kids was born after he bought the house?

A good way to start solving this puzzle is to first list all variations of three integers whose product is 36, then calculate their sums:

1 + 1 + 36 = 38
1 + 2 + 18 = 21
1 + 3 + 12 = 16
1 + 4 +  9 = 14
1 + 6 +  6 = 13
2 + 2 +  9 = 13
2 + 3 +  6 = 11
3 + 3 +  4 = 10

M knows the sum of the kids' ages (equal to the number of the bus N pointed to). Notice that all sums are unique except one, which is the sum of two different variations of three integers. Had the bus number been other than 13, M would have immediately known the answer. Because M said that he doesn’t have sufficient information to solve the puzzle, the bus number must have been 13. Now, the question remains, which of the two age variations is the correct one? Notice that in both cases (1, 6, 6 and 2, 2, 9), there are twins. The additional piece of information N provided was, “One of my kids was born before we bought the house.” The implication is that one of the kids is older than the other two, so of the two variations, the correct one is 2, 2, 9. Now, how would the solution change if N’s additional piece of information had been that one of his kids was born after he bought the house? In this case, one of the kids is younger than the other two, so the correct answer would be 1, 6, 6. Interestingly, you can solve this puzzle with a T-SQL query, as Listing A shows. (Download .Zip File)

November’s Puzzle: Crazy Sequence
This month's puzzle (acquired from Marcello Poletti) requires that you determine the next number in the following sequence.

0,
1,
2,
26012189435657951002049032270810436111915218750169457857
27541837850835631156947382240678577958130457082619920575
89224725953664156516205201587379198458774083252910524469
03888118841237643411919510455053466586162432719401971139
09845536727278537099345629855586719369774070003700430783
75899742067678401696720784628062922903210716166986726054
89884455142571939854994489395944960640451323621402659861
93073249369770477606067680670176491669403034819961881455
62519559256691883082551494294759653727484562462882423452
65977897377408964665539924359287862125159674832209760295
05696699927284670563747137533019248313587076125412683415
86012944756601145542074958995256354306828863463108496565
06827715529962567908452357025521862223581300167008345234
43236821935793184701956510729781804354173890560727428048
58399591972902172661229129842051606757903623233769945396
41914751755675576953922338030568253085999774416757843528
15913461340394604901269542028838347101363733824484506660
09334848444071193129253769465735433737572477223018153403
26471775319845373414786743270484579837866187032574059389
24215709695994630557521063203263493209220738320923356309
92326750440170176057202601082928804233560664308988871029
73807975780130560495763428386830571906622052911748225105
36697756603029574043387983471518552602805333866357139101
04633641976909739743228599421983704697910995630338960467
58898657957111765666700391567481531159439800436253993997
31203066490601325311304719028898491856203766669164468791
12524919375442584589500031156168297430464114253807489728
17233759553806617198014046779356147936352662656833395097
60000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000
00000000000,
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