## Friday, November 18, 2022

### Coyote sighting

Spotted early this morning walking west down our street, just as Bodie and I were leaving for our walk. Already too distant to be distinct by the time I managed the photo, I have added a helpful arrow. At the bottom of the shot are some of the two dozen bags of leaves where our driveway meets the road, ready for today's yard-waste pickup. Resourceful squirrels will tear the paper off the bottom of the bags in order to steal the mostly dry leaves. I've had to re-bag one of them because it was beyond repair.

## Wednesday, November 16, 2022

### Paper delivery

Looking east up Denison Rd. W., at the spot where it curves south, I believe I recognize the newspaper delivery driver's tire-tracks in this morning's freshly fallen snow.

## Saturday, November 05, 2022

### Tuva

I've been watching VagaBond for a while now. His videos provide welcome counterpoint to the tragic criminality of Russia's invasion of Ukraine, and this one, in Tuva, is better than the usual freighthopping fare.

## Friday, November 04, 2022

### Twin concatenations

Éric Angelini came up with this idea of listing products (one per line) where the multipliers introducing the line are the positive integers and the smallest possible multiplicands (after the initial line) are deduced from the products, given that the concatenations of the products (to the right of the equal signs) must be the same as the concatenations of the multipliers and multiplicands (in order, to the left of the equal signs), from the beginning, as far as it will go.

On the MathFun mail list, Éric shared Gilles Esposito-Farese's version that makes the multipliers the nonnegative integers (up to 50), instead of the positive-integers versions shown on Éric's blog:

0 * 0 = 0
1 * 0 = 0
2 * 5 = 10
4 * 63659 = 254636
5 * 119 = 595
...

For some reason Gilles skipped 3. Which makes his output for lines 4 to 50 incorrect. Ouch!

Here is my correction:

0 * 0 = 0
1 * 0 = 0
2 * 5 = 10
3 * 846 = 2538
4 * 1 = 4
5 * 1283 = 6415
6 * 2 = 12
7 * 1194673 = 8362711
8 * 118342264792783 = 946738118342264
9 * 88 = 792
10 * 7839881 = 78398810
11 * 7127164651933786 = 78398811171271646
12 * 432781551 = 5193378612
13 * 332908885487176222196 = 4327815511333290888548
14 * 512587299724651848 = 7176222196145125872
15 * 664831 = 9972465
16 * 11550979 = 184815664
...

Here is my listing up to 1000. Please let me know if you see an error!