Maths teaser. Cube numbers.

[Louis Balfour]

The sum of two consecutive cube numbers is 341, what are the cube numbers?

Don't Google it, you will get different answers.

Show your working.


I ask because my 13 year old has just returned from school having been told his answer was wrong. He has shown me his thinking and I can see his argument. I also realise that he is significantly better at maths than me...

[thebraketester]

5^3 + 6^3. So 125 and 216

Or have I fallen into the trap?

Edited by thebraketester on Thursday 3rd December 17:23

[Louis Balfour]

thebraketester said:

5^3 + 6^3

Or have fallen into the trap?

That is what teach said is the correct answer.

I didn't go to school the day they did "numbers" but even I think he is wrong.

[anonymous-user]

Technically, aren't they supposed to be in brackets or am I being a div?

[Mr Pointy]

What's a cube number?

[2 sMoKiN bArReLs]

Mr Pointy said:

What's a cube number?

How many sugars you take in your tea

(sorry, it the number times itself times itself)

[deckster]

I'm failing to see the ambiguity or alternative answer. Can you enlighten us?

[Pumpkinz]

thebraketester said:

5^3 + 6^3. So 125 and 216

Or have I fallen into the trap?

Edited by thebraketester on Thursday 3rd December 17:23

That's correct. Come on OP, publish what your son thought it was and why. I've seen some clever maths tricks in my time, but think this is pretty cut and dried unless I have really lost my skills.

[Pumpkinz]

flashbang said:

Technically, aren't they supposed to be in brackets or am I being a div?

Nope, exponent is higher precedence that adding, therefore you calculate both cubes first then sum them.

[thebraketester]

Unless it’s the cube root of 170 and 171? Which is bks IMO.

[akirk]

I would have said the same - 5 & 6 are the numbers being cubed to get a sum of 341, so the answer is 125 and 216
but it may be one of those where the interpretation of the english is just as important and I think could lead to confusion here...

a cube number is a whole number which is the cube of another whole number - and that needs to be clear...

cube numbers go:
1,8,27,64,125,216,343, etc.
so, 125 and 216 are consecutive in the list of cube numbers even though they are not consecutive numbers, they are 'consecutive cube numbers'

however I can see that to a child, 5 & 6 look a lot more consecutive than 125 and 216 - so may expect a child to answer 5 & 6 if they misunderstand...

[SS2.]

thebraketester said:

Unless it’s the cube root of 170 and 171? Which is bks IMO.

That follows the question (a cube root doesn't have to be an integer), but pretty sneaky if that's what teach was looking for.

[akirk]

SS2. said:

thebraketester said:

Unless it’s the cube root of 170 and 171? Which is bks IMO.

That follows the question (a cube root doesn't have to be an integer), but pretty sneaky if that's what teach was looking for.

no, because as I put above...
a 'cube number' is a whole number whose cube root is also a whole number...
it is a 'child learning maths' concept

so, while it is neat, 170 & 171 doesn't work...

[Louis Balfour]

So we are agreed that there are two different correct answers, and that the teacher's answer was incorrect?

[Ayahuasca]

5&6

[bigandclever]

Louis Balfour said:

So we are agreed that there are two different correct answers, and that the teacher's answer was incorrect?

Let’s have a look at the actual question.

[Bill]

Louis Balfour said:

So we are agreed that there are two different correct answers, and that the teacher's answer was incorrect?

If he is saying 5&6 then yes, because they're not cube numbers they're just the numbers you need to cube. Unless the question asks for the root of the cube numbers...

If your son is saying 125 and 216 he's right.

AIUI at least.

[Paul_M3]

Louis Balfour said:

So we are agreed that there are two different correct answers, and that the teacher's answer was incorrect?

No, I think we’re all agreed that from the way the question is worded in the OP it’s got to be 125 and 216.

[robsa]

Louis Balfour said:

So we are agreed that there are two different correct answers, and that the teacher's answer was incorrect?

It appears that the answer is correct, it’s his question that’s wrong!

Maybe ‘The sum of two consecutive integers cubed is 341. What are the two integers?’ Would have been more clear?

[2 sMoKiN bArReLs]

thebraketester said:

Unless it’s the cube root of 170 and 171? Which is bks IMO.

That's just "the sum of two consecutive numbers is 341" as all numbers have a (non integer) cube root.

The answer has to be 5 & 6 shirley?

(Or is it an Eats Shoots & Leaves scenario? )