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February 26, 2007
As The Brain Turns
I've ordered Gelfand's Algebra, to work through myself. And, to throw problems at my kids when I can't resist.
Here's the problem I gave them today, after I solved it. I'm embarrassed to say that I couldn't solve it without a hint - embarrassed, because after you see how to start it really is blindingly obvious:
You have a six-digit number that begins with "1". If you take the "1" off the beginning and place it on the end, the resulting number is three times the first. What are the other digits in the number?
Tick ... tick ... tick ... that's the wind whistling through my brain. It *is* easy. Once you figure out how to start.
I showed Connor and Aidan how to set up the problem, and even then it was difficult for them to solve. They both solved it, eventually, with lots of prompting. Connor got the concept faster, but he's lazy with arithmetic and so had more errors to backtrack and fix. Aidan was slower to get the concept, but once he did his arithmetic was impeccable. Typical. And so we spent all morning on this one math problem. Lately I've lost sight of the fact that one morning struggling with one problem often means more than any amount of plugging through curriculum..
I'm also about to order Introduction to Number Theory. I'm excited about this book. It looks, dare I say it, fun.
I'm picking my Henle back up as well. I've let my brain be idle for too long. This is not about me shoving texts at the kids and telling them to do the work; this is about educating myself as well, and showing them every day that education is a lifelong activity.
Posted by lynx at February 26, 2007 11:32 AM
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Comments
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I began by reasoning that the last digit had to be a 7, because it's the only digit which, when multiplied 3, ends with a 1. I then went to the other side, and determined that the second digit had, when multiplied by 3, to begin with 1. That left 4, 5, or 6. From there, it was a process of elimination.
Posted by: Jeff Medcalf at February 26, 2007 7:58 PM
OK - I was going in the right direction. Don't tell the answer yet. Jeff's reasoning has helped me. Can someone come sit on my kids and let me think clearly for an hour or so?
And, I'm with you, I love learning this stuff and it's funny how the kids just kind of join me. We're really, really liking Henle's Latin right now. It's been a lot of fun so far (we started in January). I hope you like it as well.
Posted by: Amy at March 1, 2007 12:37 AM
Interesting problem! But you can also solve it algebraically. Let "X" be the five digit number that is common to both numbers, then:
3*(X+100,000)=10X +1
Works like a charm!
Posted by: RedHen at March 2, 2007 8:37 AM
(Not related to the post, but I didn't feel up to looking for the Borg Cube cake post.)
I don't know if your family are into Doctor Who at all, but I recently came across this cake, and thought of you:-)
Posted by: Fe at March 7, 2007 11:24 PM