6
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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!

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  • $\begingroup$ no square roots? $\endgroup$ – Bass Jul 13 at 19:24
6
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11 for 1492:

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

10 for 1969:

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

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