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Don't be too frustrated! Hints are just that - they're not answers. And they have an annoying habit of telling you what you've already worked out, when what you wanted was the next step. Sorry and all that! Remember that you can e-mail for solutions if you're really desperate.
1. You possibly observed that the top angle of the triangle (the
obtuse one) needs to be split by at least one of your lines, in
order to make it into two or more acute angles.
2. You possibly also convinced yourself that any line that crosses
the triangle creates one acute and one obtuse angle when it reaches
a side.
It would be very wrong to assume that statements (1) and (2) are in any way contradictory!
Remember that as well as numbers like '5' and '7', there are also numbers like 1,234,567,890, …. and numbers like 0.123456789…
There are only three twenty-digit powers of 2 (264, 265 and 266) so it is possible to prove this by exhaustion (yours, that is!). However, to state the obvious, if a twenty-digit number does NOT have three repeated digits, then it has precisely two each of 0, 1, 2, …. , 9. Think about digit-sums!
Hint for Triangle puzzle
Hint for Sevens puzzle
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