A pretty neat counting problem from Mathcounts

The boys came back from a 2 day camping trip today. I had some afternoon meetings, but luckily they got back early enough for us to do a little counting project.

Without anything in particular planned, I just picked the first problem in the challenge problem section at the end of chapter 2 in our Introduction to Counting and Probability book. The problem is a pretty neat case by case counting problem (even though it looks fairly dull at first glance):

How many positive integers between 24 and 125 have a digit sum that is a multiple of 7?

The boys did a nice job of breaking the problem up into cases right away. In the first video we look at the cases where we have a 2 digit integer. I really liked hearing my younger son talk about the two digit numbers whose digit sum is 14 – it is fun to hear a young kid bring together the ideas you need to work through this problem. One of the nice surprises about this problem is that there’s some interesting number sense ideas hiding inside of it!


In the next video we look at the three digit numbers from 100 to 125 whose digit sum is a multiple of 7. There’s a little surprise in this part, too, since there are no numbers in the range with a digit sum is 14. It takes a moment for the boys to realize that the largest digit sum isn’t necessarily the largest number, so that’s a another neat math idea hiding in this problem:


So a nice problem with a couple of neat ideas beyond the case by case counting. Fun little project to do in the lucky extra 15 minutes I had with the kids today.

10 number 10’s

[not a math post – this one is about ultimate]

Yesterday I had a 6 hour drive and for part of it was sort of day dreaming about how great it would be if women’s ultimate could get as much great publicity as the US women’s soccer team did. After seeing post after post about Carli Lloyd I thought about all of the great #10’s in women’s ultimate. Saw lots of them play this past weekend. In no particular order:

(1) Fury’s Gen Laroche

7 club championships + 3 world championships. Oh, and did you know she’s been on Sportcenter’s top 10?


(2) Riot’s Shira Stern:

She’ll be representing the US on the U23 team in London next week, and this is her 2nd time on the U23 team! You can follow the U23 teams at the World Championships here:

Skyd Magazine’s U23 coverage

And then 30 minutes after publishing this post, Shira’s grab in the US Open finals gets a Sportscenter top 10 nomination:


(3) Brute Squad’s Amber Sinicrope

So happy to see her returning to Brute this season. Even with the year off, I think she’s the active “most seasons with Brute” player. I have her Amherst high school jersey hanging on the wall of my study – from her pre- #10 days 🙂


(4) Scandal’s Jenny Fey

Guess who led the US Open in combined goals (13) and assists (23). Come on, take a wild guess . . . .

US Open stats on the right hand side

(5) Phoenix’s Michelle Ng

Before Qxhna’s All Star Ultimate Tour the biggest fundraiser I can remember in ultimate was this:


I saw Liên Hoffmann wearing her Without Limits jersey at the Harvard stadium on Monday! There are not enough ways to thank Michelle for all she’s done for ultimate.

(6) Speaking of Qxhna – she wore #10 in college, for the Beach World’s team, and on Brute Squad last year:

Please support her All Star Tour if you haven’t yet:

The All Star Ultimate Tour

and watch her incredible Callahan video, too:


(7) Another #10 super star from college who is crushing it in club right now is Ozone’s Sophie Darch. Here’s her awesome Callahan video from last year:


(8) One #10 we’ve not been able to see yet this year is former Molly Brown captain Lindsey Cross.

She had a nice interview a few years back on Ultimate Interviews:

Lauren Boyle and Lindsey Cross Interview

and also kicked off Molly Brown’s awesome twitter roster announcement this year:

(9) One other #10 (who may not be wearing #10 this year, I’m not sure) that we’ve not seen yet is former #10 for the Capitals and current Traffic player Kathryn Pohran. I’m very happy to see her back after an awful knee injury at ECC last year.


(10) Who’s the 10th #10? Who did I forget on my drive last night? You tell me!