This is another number formation question. You must use each of $2$, $1$ and $8$ exactly twice to make the number $2018$. The rules are
- Allowed symbols: $+$, $-$, $\times$, $\div$, $($, $)$, $\sqrt{\quad}$, $!$. Arbitrary functions (such as the logarithm) are not allowed.
- The ordering of the numbers are not important.
- It is OK to use numbers as superscript (exponent or the power for the radical symbol).
- Concatenation is allowed although using $(2+1)1$ to construct $31$ is not allowed.
- Ceiling or flooring is not allowed. $211\div2=105.5$, not $105$ or $106$.
The use of decimal point or scientific notation is not allowed.
For example, $$(2+8)\times(2+1)!\times\sqrt{1+8}=180$$ is a valid construction, although this is not a solution because it does not equal $2018$.
Edit (after slvrbld posted his answer): Try to make $2108$ and $8102$ as well if you can.
(And of course, the more ways the better).
Second Edit I am thinking whether I can make all 4-digit numbers composed of 2, 0, 1 and 8 (numbers beginning with 0 do not count). I have solutions for some but not all of them. Once I find solution for all of them or find a well defined subset for which I have solutions, I will update it and make it a formal challenge here.
Answer
A possible solution:
$ 1\times2 + 8!/(12+8) $
Edit: more obscure approach:
$\displaystyle\binom{8\times8}{1\times1\times2} + 2 = \binom{64}{2} + 2 = 2018$
No comments:
Post a Comment