The footballer Pikachu

When in a sports clothing shop, I suddenly spotted a Pikachu!

Not one, but two!

At first we thought the black shirt was a high-necked one, but turns out that the Pikachu is actually on the back. This is what each shirt looks like on the other side:

I'm not a football fan, but I want the red shirt!

Good filtering method

The other day I received a survey from Shopee. In the middle of it, I found this question:

Looks like a great way to make sure the other survey answers are valid!

A slow Friday

It's time for Photo Friday again! Why? Because I have a new camera. ;)

I need to familiarize myself with the new camera settings... so Photo Friday will help me with that. Otherwise I might just snap photos of my meals every day.

Last Friday's theme was slow. I happened to be building our simulator for work, and it is really a slow process... the whole thing takes around four hours. The progress bar is a bit of a liar, because even when it shows that it is almost done, there is still quite some time to go!

Besides that, I took another photo for this theme, but in the end I decided to go with the first one. I would still like to write about the second photo though.

When eating snacks, sometimes I will use chopsticks.. firstly to keep my hands clean, and in this case, to slow down my snacking. After each bite, I put my chopsticks down, so that the next bite can only be taken after picking up the chopsticks and re-aligning them.

So this is an example of how it's done. :P

I'm still a little confused about whether or not to use flash with this camera. I feel that the photos are sharper with flash, but the colours don't look as good (the flash seems quite harsh). In any case, more experimentation is needed, so there will be another photo next week!

Sky Castle

I just finished watching Sky Castle. It has a wonderful storyline! I can't give it enough thumbs-ups...

 

Basically it is about a group of rich parents who are heavily invested in their children's studies. A number of events happen, turning each couple's lives upside-down...

 

I really liked how they fleshed out the plot and developed the characters... it makes the events really believable, brought about by each character's personality.

And I finally get to see Choi Won Young playing a good guy instead of a villain. :P I've mentioned him before, and I really liked his role in I Remember You; that left really a lasting impression!

The special number

For a while now, I have been subscribed to Mind-Benders for the Quarantined by MoMath (the US's National Museum of Mathematics). Some of the puzzles are quite difficult and cannot be solved without some mathematical theory, even though the puzzles are meant for all age groups. But some are definitely interesting, and really suitable for anyone!

The last puzzle was about a "self-referential number".

PUZZLE: Self-Referential Number
The first digit of a certain 8-digit integer N is the number of zeroes in the (ordinary, decimal) representation of N.  The second digit is the number of ones; the third, the number of twos; the fourth, the number of threes; the fifth, the number of fours; the sixth, the number of fives; the seventh, the number of sixes; and, finally, the eighth is the total number of distinct digits that appear in N.  What is N?

I tried this out and at first couldn't seem to get a number that worked. And then, during a particularly long and boring meeting, I played about with the numbers again, and suddenly hit the jackpot!

23110105 has 

2 zeroes

3 ones

1 two

1 three

0 fours

1 five

0 sixes

and 5 distinct digits: 0, 1, 2, 3, 5

The puzzles are sent out on Sundays, with a hint given on Tuesday, a push (aka additional hint) given on Thursday, and the solution on Saturday.

The hint came:

HINT: Iteration can work magic.

It made no sense to me, but I had already found the solution, so I was just waiting to see what method they would give to get the solution.

PUSH: What happens if you try some random 8-digit number, count zeroes, etc., to get a new 8-digit number, and then try again on the new number?

This made me try out the iteration that they mentioned. In my earlier attempt, I had already ruled out having any digits above 5 in the first seven digits (if there are six of a certain digit, we wouldn't be able to fulfill the other requirements, because the total of the first seven digits can be at most eight). So I started with a number without any of those bigger digits.

My iterations:

12303241

12221005

22300104

31211005

23110105

23110105 --> same as the number before it!

 

So this method does work... but why?

 

Unfortunately the solution to the puzzle does not even tell us why! They showed us the iterative method that I used above, and their comments were:

 

But why should this work in a reasonable number of steps?  Indeed, why should it work at all?
Sadly, I don't know.  This method does not work with all problems of this type.  But it is surprisingly useful — a great weapon to have in your armory.
(Thanks for probabilist Ander Holroyd for creating and contributing this puzzle!)

They also said "It's pretty tough to work out N by reasoning" before giving the iterative method as the "easy way", so I guess I shall just give myself a pat on the back for somehow finding that number, and just leave it at that. :P