Maths question on the 1% Club last night (with spoiler)

[AgentPidge]

The question went something like this:

If you write out the numbers as words, take the lowest three-letter, four-letter and five-letter words. What is the highest number you can make with these three numbers?

So I thought ONE, FOUR, and THREE, so the biggest number is 431.

But that was wrong - it's 301. The answer was that the three numbers are ONE, ZERO and THREE.

I googled and it says that zero IS a number. But who starts counting at zero? What do you think? I know nothing about maths, btw.

Zero is a number (or integer), although it doesn’t hold a positive or negative value. If you think of zero like the starting point. A bit like a bank balance. You don’t start necessarily at £1 or 50p and you can go into the negative too!

310 surely by their rules?

Isn’t it 310?

Zero hasn’t always been accepted as a number, if we go back to ancient times, but it is now.

I don't understand why the answer isn't 310?

It would be 310, unless there was something in the question that prevented it. Like it not being allowed to be a multiple of 10? Or needing to be odd?

I was caught out by zero too.
I should have known better.

Oh sorry, yes! My mistake.

I made a mistake. It was 310.

It is. My mistake - sorry.

But if you were to write out "numbers", would you start with zero, or one?

Depends what purpose I was doing it for I suppose.

I am a secondary school maths teacher so mainly when I write numbers for children to add/subtract from it would be either horizontally or vertically and have zero in the middle and going in both positive and negative directions.

If the wording in your OP is correct, zero is the "lowest" four-letter number. 310 is correct (I would've got 341 though!)

This sounds like a question where the exact wording might matter. If you start at 1, how do you know when to stop? The ‘natural’ way to count might be 1-10 but 10 doesn’t work with the rest of the question - they want all the single digit numbers. And in that case zero is needed for the full set.

I got caught out with that too and slightly irrationally thought I’d been had as it wasn’t (to me…) very clear.

That's a really sneaky question. I'd have gone for 1, 3 and 4 too.

If somebody asked me whether zero is a number, I'd say yes but it's natural to start counting at one.

I was also very confident with 431, I'd never have thought to include zero. It did feel a bit of a trick question.

It's questions like this that are the reason why things like MENSA tests are so unreliable. So much of the time it's a gotcha rather than testing cognitive ability. It shouldn't come down to semantics of whether zero is a number - which some would argue depends which definition of "number" you're currently using.

I understand you didn't get this question from a mensa test but I remember doing them as a kid and they were often like this. I remember my mum being really proud when I got a moderately high score but even at the time I felt it was really silly.