My first guess is at least 4 since the binomial expansion will have terms that end in a lot of zeros. Maybe just 4 but maybe I'm overlooking something and its a lot more.
Working backwards through the binomial expansion of (10+1)^1000 is a bit tedious but gets there:
1^1000 = 1 (the -1 will make this zero)
C(1000,999)*10 = 10000 (4 zeros)
C(1000,998)*10^2=49950000 (4 zeros)
C(1000,997)*10^3=...67000000 (6 zeros)
C(1000,996)*10^4=...24750000 (4 zeros)
all other terms end with have 5 or more zeros, so 11^1000 ends with
...60001
The answer is just 4.
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Posted by Jer
on 2024-04-05 11:39:59 |
Solution
