Digits with four fours

Logic Level 2

Can you write all digits from 0 to 9 by concatenating, multiplying, dividing, adding, subtracting or putting parenthesis on only 4 fours?

Example: $15 = 4*4 - \frac{4}{4}$

Yes No

2 solutions

João Areias
Dec 5, 2017

One way is:

$44 - 44 = 0$

$\frac{44}{44} = 1$

$\frac{4*4}{4+4} = 2$

$\frac{4 + 4 + 4}{4} = 3$

$4 + \frac{4 - 4}{4} = 4$

$\frac{4*4 + 4}{4} = 5$

$4 + \frac{4 + 4}{4} = 6$

$\frac{44}{4} - 4 = 7$

$4 * \frac{4 + 4}{4} = \frac{4*4}{4} + 4 = 4*4 - 4 - 4 = 8$

$4 + 4 + \frac{4}{4} = 9$

Bonus

$\frac{44 - 4}{4} = 10$

$\frac{44 + 4}{4} = 12$

$4 * 4 - \frac{4}{4} = 15$

$\frac{4*4*4}{4} = 16$

$4 * 4 + \frac{4}{4} = 17$

$4 * (4 + \frac{4}{4}) = 20$

Nice Problem and Solution!

However, the problem has a small typo: it says that 4*4+4/4 = 15 when it should be 17.

Siva Budaraju - 3 years, 6 months ago

Thanks mate, I fixed it

João Areias - 3 years, 6 months ago

$4-\frac{4+4}{4}$ is equal to 2 not 4

Kenny O. - 3 years, 6 months ago

Sorry, I copied wrong from my notes, it supposed to be $4 + \frac{4-4}{4}$ thanks for pointing that out.

João Areias - 3 years, 6 months ago

Pegajoso Piston
Jan 8, 2018

It is all possible without concatenation!

$4-4+4-4=0$

$\frac {4}{4}+4-4=1$

$\frac {4}{4}+\frac {4}{4}=2$

$\frac {4+4+4}{4}=3$

$\frac {4-4}{4}+4=4$

$\frac {4\times4+4}{4}=5$

$\frac {4+4}{4}+4=6$

$4+4-\frac {4}{4}=7$

$4\times4-4-4=8$

$4+4+\frac {4}{4}=9$