## Thursday, June 12, 2008

### NPR Sunday Puzzle (Jun 8): 5-Digit Sequence

NPR Sunday Puzzle (Jun 8): 5-Digit Sequence:
Q: A calculator displays a five-digit number. The first four digits are 8735. These digits form a logical sequence. What is the fifth number in the series?
I was led down the wrong path initially because I didn't read the puzzle carefully. There's an important clue in the question which you'll see if you are bright.

Edit: The key to the puzzle was to realize that these digits were on a calculator. I mentioned that in my clue along with the additional hints of "LED", "see" and "bright". I mentioned the word "segment" in one of my comments too.
A: The next digit is also 5. Each digit is the number of LED/LCD segments that are lit in the prior digit.

1. I enjoyed this one - 2 different ways to approach the logic!

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3. At first I thought maybe he was trying to spell BLESS backwards. But no, that's just silly of course. I enjoyed this segment a lot.

4. Assuming my answer is correct, these should be clues:

06
125
25
35
4
5
6
735
8735
96

5. Initially, I thought i was alone in my thinking but l8ter I realized that the answer is universal if you isolate your thoughts.

6. I post the puzzle every week on my blog and invite the world at large to email me for a hint.

This week is shaping up to be quite interesting, as the puzzle appears to have at least two correct answers. One involves arithmetic (and can be arrived at via two different methods), the other a matter of wordplay.

Separately, I have no idea what Vincent or Richie is driving at above.

A cool week on the Shortz front. I like it when unintended answers prove just as correct as the intended one.

7. On the air Will Shortz
"easy" and "elegant." The

8. I didn't listen to the segment on the air, but the answer IS simple and elegant. I can see that at least a couple people have got the right idea.

9. Ipso facto my answer is
WRONG!!!

10. I like Vincent's clues. We're on the same page.

11. i mental midget such as myself has no idea what the heck vincent is talking about.

12. I just came back from the BAR and I got it.

I had to look a lot closer at the BAR LIGHTS but there is answer is right in front of your face. It's as easy as 255456376

13. I've posted the simple and elegant answer which I believe must be the intended answer. I bet clues from people like Vincent now make sense. I'd be interested to see what people thought the "other" answers were.

I initially went down the path of looking at the names spelled out in English. When sorted by descending length and alphabetically you get: eight, seven, three, five, four, nine, zero, one, six, two. Did anyone get misled into thinking that?

14. Yes, some people did.

Others attacked it arithmetically, as follows:

8 + 7 = 3 x 5
7 + 3 = 5 x ?

Also,

8 - 3 = 5
7 - 5 = ?

The first thing I did was draw the LED versions of each number, but it never occurred to me to count the lit bars. I was stuck looking for repeating patterns for each given bar. Just never got on track.

You could make a principled argument that the above math approach and/or the alphabetical approach should be given credit, as each of them also forms a logical sequence. They might not be quite as elegant as Blaine's answer (which was presumably the intended one), but are surely worth considering as alternatives.

It's funny how we keep vacillating from super-easy to super-tough. The Harrison Ford puzzle was of moderate difficulty, but most of everything else in the past six weeks or so has been either pretty easy or nearly impossible for the typical solver.

I got quite a few emails this week and a spike in blog traffic as a lot of people around the country (and overseas) were looking for clues. Unfortunately for them, my email hints were mostly about the above two approaches, although I did allude glancingly to the existence of the LED answer (which I didn't know yet myself).

15. I didn't go far enough to check the SEQUENCE and hence ignored Blaine's very good clues. Better luck next week!

16. I have two calculators.
Both have sevens with
FOUR segments.

17. LOOK AT THIS:
If you express the progression as written words rather than numeric digits:
EIGHT,
SEVEN,
THREE,
FIVE,
FOUR,
NINE,
ZERO,
ONE,
SIX,
TWO, or 8735490162;
Number of letters per word in alphabetical order.

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19. aj, that's pretty much what blaine described in his last comment.

It's a good sequence to go by, but of course it didn't have anything to do with being on a calculator, which was a subtle part of the puzzle.

Segment, pfft. *I* mentioned it first. heh :P

20. A.J., Blaine has already addressed that solution. I think the explicit statement that these numbers are displayed on a calculator indicates that Blaine's final suggested solution is the one they were looking for.

21. I completely missed Happy Steve's "segment" clue the first time I read his post. Perhaps it stuck in my subconscious and made me use it later. :-)

22. I recived this question for my math fair problem, the answer i got was 5 because i counted the the lits in each number, so=ince there would be 7 lits in the number 8, the next number is 7, because there are 3 lits in the number 7, the next number is 3, there is 5 lits in the number 3, therefore the next number is 5, and there is 5 lits in the number 5 so the last number is 5
8 7 3 5 ?
8 7 3 5 5
is this correct?

For NPR puzzle posts, don't post the answer or any hints that could lead to the answer before the deadline (usually Thursday at 3pm ET). If you know the answer, submit it to NPR, but don't give it away here.

You may provide indirect hints to the answer to show you know it, but make sure they don't assist with solving. You can openly discuss your hints and the answer after the deadline. Thank you.