Y8 maths

[knowsnowt]

Is this a trial and error solution or is there a way to work it out logically?

It's probably going to be a bit of both.

It might be easier to think of it as BEN = (B + E + N) x B x E x N.

Focus on the right-hand side. If I try the smallest possible options for B, E, N then that would be 1,2,3, but (1 + 2 + 3) x 1 x 2 x 3 = 36 which isn't even 3 digits.

If I try the largest possible options that would be (9 + 8 + 7) x 9 x 8 x 7 = 12096 which is too big. In fact, 9,8,1 is still too big.

The other thing to start thinking about is multiples. The number BEN must be a multiple of B and E and N.

That's a start...

ooh.
That's a fun question (which would be way beyond the capability of my y8).
Let me think ...

I did trial and error - took 3 goes...

4, 5, 6 BEN= 1800 =way too big, so numbers are smaller.
2, 3, 4 BEN=216 almost right
1, 3, 5 BEN=135 bingo....

Well done Beyond very impressed!

I was about to say that I would knock up a quick program to go through the options if I still had access to such technology.

Thanks all 👍🏻

@TeenTimesTwo - try a spreadsheet - like this... (which proves that @BeyondThePage solution is the only one)