Daniel Barkowitz | February 20, 2007
"Math Fun (updated)"
From this week's entry on NPR's Sunday Puzzler, and something to while away the time while you are awaiting your decision:
Challenge for February 18: The object of this challenge is to develop nine different mathematical expressions that equal eight. You must use the digits 2, 7 and one other. And that other digit must be a one in the first expression, two in the next expression and so on, up to nine. You can use a digit once and only once in each expression.You may use the four arithmetic symbols: plus, minus, times and divided by, as well as exponents and decimal points. You may use parenthesis as you need them. For example: Using the digits 2, 7 and 1 you can make the expressions 2+7-1= 8.
This week's Challenge is from Robert Waynewright in New Rochelle, N.Y.
In about 3 minutes I got the first four and the last one, and I am working through the rest. Want to take a crack at it? If you can get the answers done, post them here and you may even be selected to play some word/number challenges on the radio with Will Shortz.
UPDATE!!! (And spoiler alert!) Contest is over! I have posted my answers in the comments below. Anyone have anything different?
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Responses To This Entry:
(Please note that comments are closed after 30 days to reduce spam.)First Post!
Posted by: Snively on February 20, 2007 07:29 PM
And now that I've actually read this post, I am DEFINITELY going to mess around with this puzzle. We'll see how it goes!
Posted by: Snively on February 20, 2007 07:32 PM
It says you can use decimal points: does that mean you can do things such as ***REMOVED THE ANSWER*** or ***REMOVED THE ANSWER***? If so, then I think I have them all.
Posted by: Feldman on February 20, 2007 07:46 PM
Feldman you rock! Although your nine example doesn't work. I have them all now except the 7 answer.
Posted by: Daniel Barkowitz on February 20, 2007 07:52 PM
I am a bit tired... what is wrong with the nine example? Can you not use decimal points just in between two digits (ala ***REMOVED THE ANSWER***)? Or can you not use a decimal point directly next to a operator (the ***REMOVED THE ANSWER*** )?
Posted by: Feldman on February 20, 2007 08:10 PM
Alright! Sounds like fun. :-)
I've figured out all of them except the one for 7 as well.. Hmm...
Posted by: Adam S. on February 20, 2007 08:10 PM
I got it!
***REMOVED THE ANSWER***
Posted by: Adam S on February 20, 2007 08:16 PM
Just my stupidity. I read your answer as + .9 not / .9 -- OOPS!
I have a different 7 answer... (and a different 9 answer).
I'll post my answers on Thursday (as we need to allow people to enter the contest -- deadline Thursday 3:00 eastern!)
Posted by: Daniel Barkowitz on February 20, 2007 08:22 PM
Wow, that was excellent fun! Please let us know if you find out about any other puzzles like this.
I shouldn't have posted my actual answer to the 7 one, though. Could you possibly remove it so that other people have a chance to think about it?
Posted by: Adam S on February 20, 2007 08:29 PM
I had the same answer to seven as Adam.
Posted by: Feldman on February 20, 2007 09:00 PM
On the 9 example I just did ***REMOVED THE ANSWER***
Posted by: dale on February 20, 2007 10:08 PM
that 7 solution is awesome, that was the only one I couldn't get
Posted by: Anonymous on February 20, 2007 10:10 PM
To preserve the fun, I have removed all references to answers from the above posts. OK, y'all, figure it out! And enter the contest on NPR.org when you get your answers... You could win all kinds of cool stuff. Look here for answers on Thursday at 3:00 Eastern!
Posted by: Daniel Barkowitz on February 20, 2007 11:16 PM
Woot MIT! This article is so true, the OpenCourseWare with Professor Lewin definitely convinced me to apply...
Posted by: Alyssa on February 20, 2007 11:45 PM
jeez. I got the first few quickly and spent the last fifteen minutes or so trying to figure out the 7 solution. Finally got it :D
awesome.
Posted by: Jenny Li on February 21, 2007 12:02 AM
Yes! got them too! haha. number 7 and 9 did give me the most problems. ironically enough, i did this puzzle in between problems on my partial fraction decomp homework. =P
Posted by: Josh V on February 21, 2007 12:24 AM
1, 2, 3, 4, 6 and 9 came easily. The other 3 I'm working on. I know I'm not going to be able to stop until I have the solution.
Posted by: Guyomar on February 21, 2007 03:15 AM
Madman's Solution:
***REMOVED THE ANSWERS***
Posted by: The madman who makes people fly aka Captain SS Wandering Albatross on February 21, 2007 04:44 AM
Is it legal to put a bar over a decimal point? Like .9999999999999 = .9bar (= 1)?
Posted by: Jeff on February 21, 2007 09:17 AM
Madman, took your answers off to preserve the mystery (but all of them look good to me).
Jeff, hmm, interesting thought. I don't know...
Posted by: Daniel Barkowitz on February 21, 2007 09:24 AM
I'm, sure i got all the answers except number seven. not to sure bout that one. Otherwise really enjoyed this puzzle.
Posted by: Chessy on February 21, 2007 10:56 AM
I got some of them:
***ANSWERS REMOVED***
I will be working in the others.
Mohammed
Posted by: Mohammed on February 21, 2007 01:13 PM
Yeah I got all of them!!!!!!!!!!!!!!!!!!!!!!! yeah.
I don't know if a Bolivian can participate in the contest but anyway I already sent my answers.
Mohammed
Posted by: Mohammed on February 21, 2007 01:40 PM
Go and line up for the lottery. [yoohoo] I am not going to sign for that. I don't like to be questioned on the phone. But maybe you like...
***REMOVED THESE ANSWERS***
Posted by: Saman on February 21, 2007 03:47 PM
Sorry , I didn't know we should not post our answers here.
Posted by: Saman on February 21, 2007 03:52 PM
i'd say 7 and 6 were the hardest.
Posted by: Peter on February 21, 2007 05:24 PM
stuck on 4 and 8 =)
Posted by: Melissa '11 on February 21, 2007 11:58 PM
Can we move the decimal the other way (ie 7 becomes 70)?
Posted by: Melissa '11 on February 22, 2007 12:24 AM
Nevermind, I got it another way =) I'm done!
Posted by: Melissa '11 on February 22, 2007 12:42 AM
I do enjoy math puzzles.
Unless they involve geometery. I got jipped in that subject let me tell you. If it wasn't for my lack of geometery skills I could have done decent in the AMC this afternoon, oh well.
Posted by: Kurt on February 22, 2007 02:44 AM
Yep, sorry about posting some answers.
Here a newspaper put all the Mondays this kind of puzzle so I have some practice ;) but it still was hard.
If you need any help contact me mohammedmostajo@gmail.com
Mohammed
Posted by: Mohammed on February 22, 2007 08:53 AM
The 7th was almost definitely the hardest.
Posted by: Chandresh on February 22, 2007 01:09 PM
I thought 7 wasn't that bad,unless I did it differently =) It took me longest to get 4 and 8, but I felt stupid when I got them because they were pretty obvious =)
Posted by: Melissa '11 on February 22, 2007 06:56 PM
OK to post the answers now! The contest is closed...
My answers:
2+7-1=8
(2/2)+7=8
7+3-2=8 OR (7-3)*2=8
2^(7-4)=8
7+2(.5)=8
(7*2)-6=8
7/.7-2=8
7.8+.2=8
(9+7)/2=8 OR 72/9=8
Any other answers?
I was playing with 7(base 7)-2=8 if you agreed that 7 on a base 7 system is equal to a tens place, but nah!
Anyway, I didn't win the contest... Did any of you?
Thanks for playing! This was awesome!
Posted by: Daniel Barkowitz on February 22, 2007 07:59 PM
Same answers as you (for 4, I got the first one, adn for 8, I got the second one).
Question, though - Am I just having a "moment", or does (7-3)^2 = 16, not 8?
Posted by: Melissa '11 on February 22, 2007 08:37 PM
*and
Oh, and I just realized you probably meant to multiply them =)
Posted by: Melissa '11 on February 22, 2007 08:38 PM
OOPS! I did! I'll go back and fix!
Posted by: Daniel Barkowitz on February 22, 2007 09:01 PM
How about this answer for #3?
(.7-.2)^-3=8
That's assuming the negative in the exponent is alright, of course.
Another would be
3/.2-7=8
A less rule-bending way to do #8 would be to just add them up seperately.
.8+.2+7
Finally, for #4,
4/(.7-.2)=8
That's all for now, but I'll keep thinking. :-)
Posted by: Adam S. on February 22, 2007 09:47 PM
Adam, you rock my world... ;)
Posted by: Daniel Barkowitz on February 22, 2007 09:52 PM
Question is... did anyone get picked? I didn't. :-(
Posted by: akdaddy on February 22, 2007 10:19 PM
I thought Adam S.'s variations were awesome. I amused myself on my run today by realizing the problem could be extended a bit. Start w/ 0 instead of 1 and end w/ 13 instead of 9. I've posted my solutions at http://primepuzzle.com/leesnewest/make-8.html but you're not allowed to look until you've given it a shot. Of course, I'm sure Adam'll come up with some alternates.
Lee Bradley
Posted by: Lee Bradley on March 4, 2007 06:53 PM
good one - especially 7th one..
why should someone find 7th one tough... is it something related to how the brain computers or analyses it.... whizzing through five or six numbers..
suddenly what happens...neurons loose gigabit ethernet connection and acquire just a megabit EC
what about posts where 5th and 9th were tough.. effective connection between the neurons, how active..
for all math whizzes out there, what should we take care or factors for solving these problems much faster and efficient...or answers for my question is just 'a cool head'?
Posted by: anonymous on March 6, 2007 07:25 PM
For all those that remain interested in this stuff, the link I posted in my March 4th note has slightly different content than it did on March 4th. Several of the proposed solutions have been declared illegal and a few alternate solutions have been added.
Also, the correct spelling of the originator of this cool problem is Robert T. Wainwright. This fellow has been around for a while and in the early 70s edited a quarterly newsletter called LIFELINES which was a clearing house for all the discoveries people were making with John Conway's Game of Life.
Posted by: Lee Bradley on March 8, 2007 07:31 PM
And, if you liked this one, check out Robert Wainwright's
"Building Twenty"
Using the digits 2, 3 and 4 once and only once, develop mathematical expressions which equal all the whole numbers from one through twenty. You may use any of the following symbols: addition [+], subtraction [-], multiplication [x], division [/], exponentiation [^] as well as decimal points and parentheses as needed.
For example: 1=3+2-4
Posted by: Lee Bradley on March 12, 2007 02:49 PM
3+2-4 =1
2*3-4 =2
2+4-3 =3
(3-2)*4 =4
3^2-4=5
3*4/2 =6
(3-0.2)/0.4 =7
(4-2)^3 =8
3^(4/2) =9
2*3+4=10
2*4+3=11
(2^3)+4 or 2^3+4 = 12
(3^2)+4=13
4*3+2=14
3*2/0.4 =15
(4/0.2)-3=17
3*(2+4)=18
4^2+3=19
3+2*5=20
how about 16? got stuck on that...
should be simple...
Posted by: anonymous on March 13, 2007 05:31 AM
