Thursday, February 02, 2012

NPR Sunday Puzzle (Jan 29, 2012): An Equation for 2012

NPR Sunday Puzzle (Jan 29, 2012): An Equation for 2012:
Q: Write the digits from 1 to 9 in a line. If you put a plus sign after the 2, a times sign after the 4, and plus signs after the 6 and 8, the line shows 12 + 34 x 56 + 78 + 9, which equals 2003. That's nine years off from our current year 2012. This example uses four arithmetic symbols. The object is to use just three of the following arithmetic operations: addition, subtraction, multiplication and division, in a line from 1 to 9 to get 2012 exactly. The operations should be performed in order from left to right. There are no tricks to this puzzle. Can you do it?
I was just about to retire for the evening, but I figured you might need some assistance in solving the puzzle, so your help is... Gee, how do I give you a hint to a math puzzle?

Edit: The hints were "retire" (Social Security Administration = SSA = subtract, subtract, add) and "assistance" and "help" (411 = number of digits to group together, with 3 being assumed for the remaining digits).
A: 1234 - 5 - 6 + 789 = 2012

56 comments:

  1. Here's my standard reminder... don't post the answer or any hints that could lead directly to the answer (e.g. via Google or Bing) before the deadline of Thursday at 3pm ET. If you know the answer, click the link and 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 give the answer away. You can openly discuss your hints and the answer after the Thursday deadline. Thank you.

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  2. I found this puzzle on the NPR page before Blaine posted it,
    so I posted my comment as the 48th one on the page from last week's puzzle. It is a cute puzzle with a minimalist
    solution.

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  3. As our resident anal mathematician, I will point out that saying the operations should be performed in order from left to right is not actually correct, as Will's example demonstrates.

    If we were to actually perform the operations from left to right, then 12 + 34 x 56 + 78 + 9 would be calculated as {[(12 + 34) x 56] + 78} + 9, which equals 2663, not 2003.

    Obviously Will intends for us to follow the traditional mathematical order of operations, wherein we first calculate multiplication and division from left to right, and then addition and subtraction from left to right with what remains.

    Thus, 12 + 34 x 56 + 78 + 9 is calculated as {[12 + (34 x 56)] + 78} + 9 = 2003.

    However, the common mnemonic PEMDAS can be somewhat misleading since multiplication has equal weight to division, and addition has equal weight to subtraction. So, for instance, if given a line like 12/3*4, it is best interpreted as (12/3)*4 = 16, not as 12/(3*4) = 1.

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    1. And why doesn't this surprise me?

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    2. This comment has been removed by a blog administrator.

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  4. I agree with PC that the usual order of precedence among arithmetic operators contradicts Will's phrasing of the puzzle. However, there is only one answer to this puzzle and it does follow both the ordering of computations that Will stated and the usual operator precedence.

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  5. I got 2013 doing it one way! Come on Will, tell me Ed Pegg, Jr. made a mistake.

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  6. This comment has been removed by a blog administrator.

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  7. Now I am asking myself why it took me so long to get the intended answer. Tenacity rules!

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  8. as I get older I hope this kind of help stays around

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  9. I guess when solved this puzzle appears to be as simple as ╥.

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  10. The Joint Expeditionary Force Experiment

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  11. McKnight : Gospel :: Brubeck : Jazz

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  12. step one - learn three chords, step two - form a band.

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  13. This comment has been removed by a blog administrator.

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    1. I can see why Blaine might have been a little concerned about your deleted post, but I think what you posted was said by Will and shown clearly in his example. I found none of the posts at all helpful, and some very misleading. I may say more on Thursday.

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    2. You hint in that post seems too obvious to me.

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    3. No problem, maybe my hint was too obvious. No hard feelings. Wasn't sure originally if you deleted the post because of the original statement, or the hint.

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  14. It's simpler than it sounds. It's almost as easy as 1, 2, 3.

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  15. Did we lose Weinberg?

    -- Other Ben

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  16. Obviously, at least one of the allowable arithmetic operators isn't needed. Does it reveal too much to say that two aren't needed?

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  17. I wasn't going to bother with this until I read everyones comments today. Cute, indeed.

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  18. I'm just hoping we don't see this puzzle again when Will celebrates his 35th anniversary with WESun.

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  19. Blaine,

    This is f5575a18-7651-11e0-8f0a-000bcdcb471e. AIM won't let me post in the new system.

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  20. Use Occam's Razor, Grasshopper...

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  21. If I may get back to the topic of LAST WEEK's challenge, I had tried many times to post my submissions here but I couldn't get past that blasted word verification. I STILL wonder how ANYBODY was able to post any comments last week at this time!!

    Anyway, I'm glad that Blaine has fixed it, so here are the three entries I submitted last week:

    My entries:
    1. When Things Were Rotten - Then Came Bronson - Pushing Daisies - Six Feet Under
    2. It Takes a Thief - To Catch a Predator - In the Heat of the Night - When Animals Attack
    3. According to Jim - The King Family Show - Real People - Good Times - Until Tomorrow

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  22. My seven year old solved the puzzle in less than five minutes without the use of a calculator, so it's not very difficult. She insists that Feist on Sesame Street helped her with the numbers.

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  23. I think some may consider this puzzle misleadingly worded.

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    Replies
    1. My first instinct was that we had to use exactly 3 out of the 4 different operations, in other words none of them repeated.

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  24. From a precocious seven year old:

    1234 -5 -6 +789 = 2012

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  25. And in 10 years, when Will will have been the NPR puzzlemaster for 35 years, 1234 + 5 - 6 + 789 = 2022. I'm a bit surprised that Blaine let me get away with such a broad hint that there was a "-5" term in there.

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    1. I embellished your hint a little more with the chinese names "dragon, tiger, dragon, tiger" for 1234 ± 5 ± 6 + 789 = 2012, 2022, 2024, 2034

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  26. My minimalist answer to this puzzle involves moving one
    digit of the example. Move the 8 from next to the 7 to the
    other side of the + and put it next to the 9.
    The sample was 12 + 34x56 + 78 + 9 = 2003.
    The result is 12 + 34x56 + 7 + 89 = 2012.

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  27. Interesting: NPR revised the example after the fact to an equation that actually works when performed in order from left to right - http://www.npr.org/2012/01/29/146034893/this-puzzle-is-the-pits

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    1. Honestly do they think that NPR listeners don't remember the precedence of mathematical operators? It wasn't necessary to say left to right. This week's puzzle works left to right or using precedence of mathematical operators (where plus and minus have the same precedence so you would go left to right anyway). Will should just stick to words since numbers are obviously not his forte.

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  28. Blaine:
    Did you notice that the date at the top of this page is now showing: Friday, March 02, 2012 (& I cut and pasted it here)??? Man, that month went by fast! And it had an extra day this year too!

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    Replies
    1. Thanks for catching that. I picked the wrong month when making the update. It should be back to Feb 2 now.

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    2. That's a relief. There are some events I have been looking forward to this month (February) that I would hate to miss. On the other hand, it would be nice to skip a month of political rhetoric.

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  29. Here! Here! SDB. I skipped this week's puzzle and had chocolate martinis (well only one really)instead. I was leaning toward EKW's solution, kept wanting that 12 to stay intact. I should have paid more attention to Tommy Boy's "Take Five".

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    1. I would have skipped the puzzle too if it meant I could have a chocolate martini. Even I have my price.

      BTW, instead of an olive, does it have an M&M?

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  30. Dave Brubeck - "Take Five" (-5).

    Claude McKnight founded the a cappella group Take Six (-6).

    JEFX - Joint Expeditionary Force Experiment

    J=10 (1+2+3+4) E=5 F=6 X=24 (7+8+9)

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  31. The gnu puzzle is up and it took just under ten minutes this time to solve, so I think lots of listeners will get the answer this time without needing our aid.

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  32. Some alert readers my age might soon have not just one, but TWO different Hanna Barbera theme songs running through their heads.

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  33. Replies
    1. Which, I suppose, is another clue.

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    2. Well, no, but now you mention it, I can see one hiding in there somewhere. (This is mucho more fun than the stupid puzzle is.)

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  34. Then remove a poorly sun god to get yet another animal...

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  35. I'm very disappointed....I heard this when first broadcast, and decided to write a computer program to come up with the answer...Cheating you may say, but not really. I thought it would be a good exercise for expanding my Python skills. Anyway, the program I wrote assumed that the words, "use just THREE of the following arithmetic operations: addition, subtraction, multiplication and division", meant, well, use three. The answer only uses two. Did no one else find that misleading?

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    1. I read it as 3 operators from the four basic operators where they might be the same. Reinforcing this idea is the example which uses 4 operators (but only two unique ones). So I didn't read it as 3 different operators... but as 3 exactly with repeats allowed.

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    2. Agreed. Seeing the text, rather than remembering the audio, changed my mind. In any event it was easy enough to modify the program, so that it did find the right answer.

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