# How to make the two important years 1492 and 1969 with a minimum number of 1s

Using only 1s, make 1492 and 1969 with the minimum number of digits

Rules: allowed operations +, -, ×, ÷, ^, (), and ! (factorial). Concatenation of the original digits is allowed, but not (1+1)1=21. Note, the () can also be used as binomial coefficient. Example: $$\binom{11}{1+1}+1111^{11} +(11+1)!$$ The record to beat is 13 for both!

• no square roots? – Bass Jul 13 at 19:24

11 for 1492:

$$(((1+1+1)!)!+(11+1+1)\times(1+1))\times(1+1)$$
$$=(6!+26)\times2$$
$$=746\times2$$
$$=1492$$

10 for 1969:

$$(\frac{((1+1+1)!)!}{1+1+1+1}-1)\times11$$
$$=(\frac{720}{4}-1)\times11$$
$$=179\times11$$
$$=1969$$