<s>[INST] In how many ways can a batsman score a century in all $6$'s and $4$'s? A batsman scored a century in all $6$'s and $4$'s. In how many ways can he do this?
The given answer is $8$, but there is no explanation, how are they doing it?
As century is $100$ runs a very loose translation of this problem would be "In how many ways we can get a sum of $100$ by using only $4$'s and $6$'s?"
 [/INST] If you want exactly $100$ (and not $102$ or $104$, etc)
Then these are the possibilities
$10\cdot 6+10\cdot 4=100$,
$12\cdot 6+7\cdot 4=100$,
$14\cdot 6+4\cdot 4=100$,
$16\cdot 6+1\cdot 4=100$,
$8\cdot 6+13\cdot 4=100$,
$6\cdot 6+16\cdot 4=100$,
$4\cdot 6+19\cdot 4=100$,
$2\cdot 6+22\cdot 4=100$
And if you allow that no $6$'s required and he can make $100$ with only $4$'s then this is the $9$th possibility, 
$0\cdot 6+25\cdot 4=100$.
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