We can get probability $\ge 70\%$ with six 10-sided dice:
- 10 sides $=6$
- 3 sides $=11$, 7 sides $=5$
- 4 sides $=10$, 6 sides $=4$
- 5 sides $=9$, 5 sides $=3$
- 6 sides $=8$, 4 sides $=2$
- 7 sides $=7$, 3 sides $=1$
Robert Israel
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