I would like to know the tunnel number of $n$-pretzel knots. I have searched and found nothing for any $n>3$. When $n=2$, $t(K)=1$ or $2$ depending on the number of twists, which is proved in a paper by [Morimoto, Sakuma, and Yokota](https://projecteuclid.org/euclid.jmsj/1226498920). Does anyone know if this has been computed for $n>3$? I know that Yokota has a paper about estimating tunnel number using quantum invariants, but I am not sure that it will be useful here the whole class of pretzel knots. But if you know that it will be, then it would be great to know that as well. Thanks.



Tunnel number of Pretzel knots
Any pretzel knot (more generally [Monstesinos knot](http://en.wikipedia.org/wiki/Montesinos_link)) surjects a reflection orbifold in a polygon. The ranks of these groups have been [computed by Weidmann](http://doi.org/10.1112/plms/pdm018), so one may obtain a lower bound on the rank of the Montesinos knot, hence the tunnel number, using this estimate. 


