An algebra lesson from Timmy. Because I love you. And I want to stay your friend.
2016 has been a year of shocks and surprises, and I for one will be glad to see it over. I am hoping and praying that one trend will disappear next year – the horseshoe/burger/beer mathematics puzzle. Because every time I see one of these I am drawn to look at it and dismayed to find out… you’re still damn well getting it wrong!
Now, first off.
If you title your post "only for genius’s" then I will find you. I will hunt you down. And I will take away your apostrophe key until you can use it properly.
There. That’s that out of the way.
I hear a lot of people complain that they never use the algebra they were taught at school. This is very clear, looking at the answers we’re getting…but in fact you are using algebra, and you’re doing it in your head. Go you!
(Now, a caveat. I am not a mathematician. I have however got a degree in physics and electronics, including semiconductor physics, nuclear physics and particle theory. I have therefore done more algebra and arithmetic than you can shake an abacus at.)
If you apply the mathematical rules correctly, you will always arrive at one consistent answer. This answer will, in fact, be wrong. But we will look at that in a minute. Let’s try and find the answer you’re ‘supposed’ to get if you are a ‘genius’.
These puzzles always seem to take a similar form.
Line one is something like
horse + horse + horse = 30.
This is like writing [a+a+a=x] or [3a=x]. Or [a=x/3]. Where x=30. So a=30/3. Which we all manage to solve to get ‘horse’ = 10.
So far so good. Your algebra is working. Awesome!
The next line is probably something like
horse + horseshoes + horseshoes = 18
This is writing [a + b + b = y], or [a+2b=y], where y=18 and a = 10 (from line one)
So [2b=y-a], so [b=(y-a) / 2] , or [b=(18-10)/2]
Which would make ‘horseshoes’ = 4
So far so good. Your algebra is holding up nicely, even if you’re actually solving this in your head. It’s still algebra.
Same again. Something like
Horseshoes – boots = 2
We used b to represent the horseshoes, and a to represent the horse. If c represents the boots then…
[b-c=z], or [c=z-b] – which for us is [4-c=2], which makes c (boots, remember) = 2
You probably did that in your head too..
This is where it all goes to hell in a handbasket. There are two little tricks in here that mean you’ll probably get it wrong. Line four is something like
Boot + Horse x horseshoe = ?
Trick one. The first thing you might miss is that there’s only one boot, and only one horseshoe. So when boots=2, boot (singular) must be 1. If horseshoes = 4, then horseshoe (singular) must be 2.
So that line becomes
1 + 10 x 2 = ?
Trick two. Now, the evil blighters want you to forget that you don’t do arithmetic from left to right. There’s a reason for this, and we will talk about it in a minute.
There’s an order to do these in. First off deal with the brackets. There aren’t any here.. and we’ll talk about that in a minute too.
Then do the division and the multiplication from left to right.
So that’s 10 x 2 = 20.
Now do the addition and subtraction from left to right.
So that’s 1+20=21.
Always. The absolute values may vary from puzzle to puzzle, and the horses might get replaced by hamburgers, but the rules are still the same.
Horse = 10
Horseshoe pair = 4
Boot pair = 2
=> Horseshoe =2
=> Boot = 1
1 + 10 × 2 = 21
(Calculated as 1 = (10 x 2) because you have to do things in the right order according to the rules of arithmetic.)
Now. Here’s the thing. If you were a REAL genius you’d have remembered that mathematics is a way of representing the real world in numbers and symbols. Which is why the rules exist and you do multiplication first.
And real geniuses want to make sure that there’s no room for getting things wrong, so we throw brackets in like there’s a sale at the bracket store.
So, in the real world, this puzzle might at the end mean
"Multiply the number of horseshoes per horse by the number of horses and you’ll get the number of horseshoes to buy…
Then add on the number of boots to buy and you’ll have the total number of things to bring home from the chandlery. "
We obviously have a large number of two legged horses and a peg legged cowboy, but who cares.
What you can’t meaningfully do is add the number of boots and the number of horses and multiply by a number of horseshoes. That’s craziness, unless you are in the habit of putting horseshoes on your boots.
AND… we’ve assumed that a picture of two horseshoes is equal to twice as many as a picture of one horseshoe. But that’s only an assumption. In reality we worked out what the value of the symbol ‘horseshoes’ meant but not what the symbol ‘horseshoe’ meant. It might be different. (While a ‘W’ looks like two ‘V’s together, it’s a different symbol, remember. This is no different)
So the only real and true answer to these puzzles is ‘it’s meaningless’ until we know what things represent and what the symbols mean. If they mean anything.
Can we stop posting these now? Please?