Posted by: Michael | 05/04/2009

Another Math question

I tutored some kids yesterday; it was fun. I can see some people whose blogs I read laughing.

Strange mixture of questions; one question how many different pizza combinations can be made from 7 toppings. Strange the four kids I was talking to had not heard of factorials and so their only method was by listing which I thought dumb. I was told this a topic that would be covered in May.

I was impressed that they came on a Saturday and were not required to come.

Anyway one of the questions intrigues me:

What number is 6 times its digit?
Now its easy to do by enumeration:

6 12 18 24 30 36 42 48 54 60 with 54 satisfying all properties:

5 + 4 = 9
9 * 6 = 54

BUT how to arrive at the solution without enumeration.
So far I have gotten as far as:

6 (a + b) = number
a + b = c

At this point I am stuck.
Any ideas????

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Responses

  1. That’s a fun question…I can’t believe you made me do math before 7 am though, lol.

    Anyway, I don’t think there’s a c involved, the real “problem” is that you need to keep in mind what the difference is between looking at the full number (54) and the separate digits (5 and 4)…

    So, for the digits you can use a and b.
    For the full number however, a is ten times bigger (as a is actually 50, not 5).

    6(a+b)=10a+b
    6a+6b=10a+b
    5b=4a


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