Constructing integers using 4s

By Michael Latham on Tuesday, September 24, 2002 - 02:50 pm:

Is it possible to create the numbers 13, 14, 18 and 19 by using the number 4, four times only. (plus any signs or symbols you may need) The closest I have got is:

4.4 x 4 + .4 = 18

Any advances? Many thanks

By Lee L on Tuesday, September 24, 2002 - 03:27 pm:

(4 - 0.4) / 0.4 + 4 = 13

$(4 + 4 \times 0.4) / 0.4 = 14$

$(4 + 4 - 0.4) / (0.4) = 19$

By Emma McCaughan on Tuesday, September 24, 2002 - 06:18 pm:

4! (=24) and

\sqrt{4}

are both useful.

By Ian Short on Tuesday, September 24, 2002 - 09:16 pm:

4! - 4 - 4 / 4 = 19

$\sqrt{4} \times \sqrt{4} \times 4 + \sqrt{4} = 18$

$\sqrt{4} \times \sqrt{4} \times 4 - \sqrt{4} = 14$

$44 / 4 + \sqrt{4} = 13$

I'm not too sure what the boundaries of this problem are.

By Michael Latham on Wednesday, September 25, 2002 - 09:45 am:

Thanks to all contributors. Believe it or not, this problem was set as homework for a 9 year old .

By Emma McCaughan on Wednesday, September 25, 2002 - 02:22 pm:

Usually when I've set this to 11 year olds, it's been a case of "see how many of the numbers 1-100 you can do"; we've then collated answers, and then there's been a general challenge to anyone to find the last few. I certainly wouldn't worry about every individual finding every one!
There was a nice variant on this problem when I was at school - using the four digits of the year to make the numbers 1-100. It doesn't work too well now, but it was great in the 1980s.