The Maths Thread

I did find it really odd when my son was little and he came home from school to tell me that he had been told off by his teacher for doing maths in his head and not using a number line. To which I replied what’s the point of a number line.
It does irritate me that if you are shit at maths or science, then everyone says, oh it’s ok it’s hard and then dumbs it down. As opposed to nobody believing you if you are shit at art, with the normal response being that you’re not trying hard enough.
The chances are that the teacher wasn't too good at mental arithmetic, calculators have made it a bit of a dying art.
 
It says the solution is as described, and you'll always find it by the 6th day... but there are only 5 boxes... so if opened the same box every day you would always find it by the 5th day?
The hiding cat may move in either direction - say, for example, you opened box 1 all 5 days in a row.

The cat, just for example, may have started in box 2. And then moved to box 3. And then back to 2. And then 3. And so on.

With the "open the same box all the time strategy" - it's possible that you'd never find the cat.
 
The hiding cat may move in either direction - say, for example, you opened box 1 all 5 days in a row.

The cat, just for example, may have started in box 2. And then moved to box 3. And then back to 2. And 3. And so on.

With the "open the same box all the time strategy" - it's possible that you'd never find the cat.
ah I missed the 'either direction'!
 
Here's another puzzle I enjoyed - but far easier than the cat-in-a-box problem.

This is typical of the logical thinking problems now posed by top level firms in the USA.
Enjoy.

 
And here's another - not sure if I've mentioned it above but here goes.
===
Suppose you are playing a game against an adversary. The goal of the game is to amass more coins than your opponent.

Before you are 100 stacks of coins - of known but variable size lined up in a row. If it's your turn, you may pick either the current leftmost stack - or the current rightmost stack. Once picked, you place all the coins from the selected stack into your inventory. And then it's your opponent's turn - who has the same options - pick up the current rightmost stack or the current leftmost stack and then it's back to you. Turns alternate until no stacks are left.

You go first - devise a strategy whereby - at worst - you'll end up drawing with 100 stacks.
 
I'd go for 50/50.
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