This week’s puzzle is dedicated to those of you who have written me so kindly in support of the Sunday Morning Puzzle. Keep those cards and letters coming. Valentines are welcome. The puzzle is also dedicated to W. H. Russell.
What are the last two 3-digit numbers that complete, for now, the sequence below?
232, 345, 681, 013, 151, 820, 222, 529, ???, ???.
Hint: The eight 3-digit numbers above are not the real (natural) numbers of the sequence. However, the digits themselves are given in the correct order. (Please don’t be P.O.'d! If the string of digits was broken into the proper numbers I’m sure some of the first-class minds at the SDMB would immediately solve the puzzle. And where’s the fun and challenge in that?)
I don’t quite get what your hint is telling me. What exactly did you do to the sequence that would make it harder? And what do you mean by this:
By saying the numbers aren’t “natural” are you saying that the answer may involve irrational, or imaginary numbers like (-1)^1/2? I don’t think that’s what you mean, but I still don’t understand you. Perhaps you mean the numbers aren’t a set of natural numbers, but integers or whole numbers instead.
Or maybe you simply mean the numbers you presented in your post, are not the ORIGINAL numbers of the sequence. If this is what you mean, then please be more careful about the words you use when describing a math problem.
Well, to some degree I thought that the meaning of the hint should be a bit vague, after all-- it is just a hint. Misinterpreted, a hint can become a hindrance. Suffice to say, however, that there are no irrational numbers in the sequence.
The sequential stream of digits is not broken up into the correct numbers. Disregard the commas given and place them elsewhere, adding more or less as needed. And yes, I might be able to make things a little clearer still, but this is a puzzle, and I would argue a fair and solvable puzzle,** as is**. The Sunday Morning Puzzle (see #'s 1-3) is meant to take a bit of musing on to reach the solution. By the way, checking prior posts might be of help here, but not mine. That hint should best be avoided as well by those easily tricked, and I shouldn’t probably of mentioned it at all. But what’s done is done.
This is the patern that is in the numbers: 2 3 2 3 4 5 6
This is the sequence with my numbers bolded: 8 10 13 15 18 20 22 25 29 32 37 43
8-10 =2
10-13 =3
13-15 =2
15-18 =3
18-20 =2
20-22 =2 Add the last two (18-20 and 20-22 to make 4)
22-25 =3 Now here is where I got thrown off
25-29 =4
29-32 =3 32-37 =5 37-43 =6
Somewhere in my logic I screwed it up, but I do see the pattern.
Interesting analysis!
However the actual answer is not so complex. Please reread the initial puzzle–and note that the last two 3-digit numbers will complete the sequence…for now.
aseymayo Congratulations again! I see the puzzle is going to have to increase in difficulty to get by the likes of you! I tip my hat! I thought I had finally stumped this board, but Curses! Foiled by aseymayo again! Back to the drawing board.
I’ll give my explanation and Bio can add anything I might have missed.
The first clue was in the dedication to “W.H. Russell.” I looked him up and discovered he was the co-founder of the Pony Express. So I started playing with the numbers and found I kept going back to separating them the same way as robgruver - 2,3,2,3,4,5… etc. The first numbers weren’t any help, but the middle sequence seemed familiar, and thinking about them in terms of letters and delivery (from the Pony Express clue), I realized they were the rising prices of a first class US postage stamp. So after 29 cents, the price went up to 32, then 33 and it just went up again in January to 34. This also fit in with the clue that it completed the sequence “for now” - as the price will likely rise again in a few years’ time.
(I don’t know why the price went up from 2 to 3, then back down again to 2 - maybe Biotop will tell us. And if these puzzles get any more difficult, I may have to go out of town permanently!)
My understanding is that an Act of Congress actually lowered the price of postage at the time, but I’ll have to doublecheck my references when I get home from work tonight.
Other clues included the “Keep those cards and letters coming” in the dedication, as well as “first class minds” and “P.O.'d” later in the puzzle. Also in my reply to Arthur, the clue to check “prior posts” seemed to me a dead giveaway.
