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It is not practical to go infinitely in the future. So let's look at the rest of the 21st century. For those, the 1st of October is on a Friday in the following years:

2021

2027

2032

2038

2049

2055

2060

2066

2077

2083

2088

2094

2100

For the rest of the 21st century the 1st of October will be on a Saturday in these years:

2016

2022

2033

2039

2044

2050

2061

2067

2072

2078

2089

2095

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Q: What year will October 1st fall on a Friday or Saturday?
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