Here is your math puzzle for the week. Erin and I were trying to figure it out and are stumped.
Make a 3X3 grid using 9 boxes. Adding the top digits with the middle digits to come up with the bottom sum, use the digits 1-9 once in each "window" to make as many true equations as possible. Make sense? Basically, add two 3-digit numbers together to come up with another 3-digit number using 1-9 only once.
By the end of the week, Erin needs to come up with as many correct solutions as possible (and know how she got them). Anyone who wants to help with this challenge is invited to do so!
Ordinary thoughts from an Ordinary Guy
14 comments:
uhhhhhh. my math wizard arrives tonight at 10:51. i'll turn her loose on this first thing.
Maybe not FIRST thing...
Let us know what the solution to the puzzle is once Erin figures it out. I've been racking my brain, and can't for the life of me figure it out.
We will post the answer.
Her teacher just revealed one adjustment to the rules. You can carry a number and not count it in the next column (except for the last column). Maybe that will help!
I found one by brute force that complies with the rule adjustment: 192+483=675
192 + 483 = 675
291 + 384 = 675
193 + 482 = 675
391 + 284 = 675
182 + 493 = 675
281 + 394 = 675
183 + 492 = 675
381 + 294 = 675
Wow! Time has slipped by me, and I missed this post! Ugh, and she needed it by the end of the week. It looks like Deloy has come up with lots of solutions (impressive!). What I wonder now is if there are solutions with answers other than 675. I will set myself to this task! I also wonder how to determine how many solutions are possible . . . how to know when you have them all. Hmm . . .
It's almost midnight here, but I couldn't rest until I came up with at least one different one. Another possible sum is 981:
327+654=981
324+657=981
357+624=981
354+627=981
etc. just keep shifting digits in that way. OK, now I can go to bed.
Ooh - got another one - OK now I won't be able to sleep!
184+392=576
(Again, rearranging digits will give lots of different addends with this same sum.)
David is sitting here telling me there are thousands of different answers. I think he may be exaggerating, so I'm still setting myself the task of figuring out how many are possible and why.
Thanks for the problem Erin and Tony!
Although there ARE 362,880 different arrangements of those digits in those boxes, so maybe he isn't exaggerating about there being thousands of correct answers.
OK, now I really won't be able to sleep!
Couple more ...
394 + 182 = 576
194 + 382 = 576
Carrying the 1 and having it count will allow for other combinations like the ones Heidi provided ...
128 + 439 = 567
218 + 349 = 567
438 + 129 = 567
348 + 219 = 567
I've yet to find a combination that doesn't require carrying a 1 ...
Thanks for all of your work everyone! I didn't mean for anyone to lose sleep over this!
I agree that I don't believe there are any in which you don't carry the one. (That is what I was working on!)
Erin had found the 981 combinations. I'll pass along the other ones to see if anyone else figured them out.
Now, everyone, put this behind you and sleep well tonight!
Thanks!
I think it's cool how many comments a MATH post generated!
:-)
Yeah, and my book review received none. There is something just plain wrong about that!
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