Personal Blogs

For the problem see

This was new to me. I found it in Mathematical Puzzles: A Connoisseur’s Collection, by Peter Winkler.

Think of the 2023 numbers 1, 11, 111, 1111, … up to the number with 2023 digits, all 1’s. Imagine dividing each by 2022 and taking the remainder. There are only 2022 distinct remainders possible 0, 1, 2, 3, … 2021 but we have produced 2023 remainders, and thus there must be at least two of the numbers 1, 11, 111, 1111, … with the same remainder.

If we now take the smaller of the two from the larger, the number we get must be divisible by 2022, and it will consist only of 0’s and 1’s .as required.

It’s late, hope I have the details right, but you should be able to see that the argument is correct and 2022 could be replaced by any number we please.

I met this bloke who claimed he’d built a house with a thousand floors. I thought, that’s a tall story.

This surprises me!

I calculate that if all the viral particles in my garden were arranged end-to-end they would reach to the Sun.

It's estimated that each cm³ of soil contains 10¹¹ such particles, of multifarious kinds, some known to science, most not. A typical diameter for a virus particle is 10^-7 m. 

So the particles in each cm³ would stretch for 10¹¹ x 10^-7 m = 10⁴ m = 10 km.

I estimate the volume of topsoil in my garden as a bit over 15 m³, and 1 m³ = 10⁶ cm³.

That gives a distance of 15 x 10⁶ x 10 km = 150 million km, the distance from here to the Sun. 

I rediscovered this goblet at the back of a shelf. It’s something I picked up in an antique shop years ago.

I bought it for its attractive colour and grape vine design. Looking at it anew it occurred to me that it’s probably uranium glass, which has literally got uranium in it, although not very much, a few percent at most, and although it will be slightly radioactive it ought to be harmless. Uranium glass used to be quite popular but fell out of favour, possibly because the availability of uranium was restricted during the Cold War (Wikipedia).

If it is uranium glass it should fluoresce under ultraviolet, so I got a UV lamp and tried it. Wow!!! How beautiful is this? I was so excited.

Exuberant = ant no longer driving taxi

What do you call a woman that swears at tea? Kirsty.

After seeing a YouTube video "hoes this app blow out candles" about an app called 'Blower' on The Action Lab I bought a copy to try it out.

The app is a simulation of a fan and the amazing thing is that it does actually blow things about. The Action Lab showed it really ould blow out a small candle but I just tried blowing some small scraps of paper and sure enough they move.

A popular question in Christmas quizzes asks how many gifts were sent, and received, altogether in the carol The Twelve Days of Christmas.

So on day 1 (sing the song) it was 1

On day 2 (sing the song) it was 2 plus 1 = 3

On day 3 plus 2 plus 1 = 6

….

What is the total after 12 days: 1 plus 3 plus 6 …?

Now, what if there were 365 days of Christmas? What would the grand total be then?

My friend was rushed to hospital after being kicked by a horse. Luckily his condition is stable.