## 1995-12 Solution

- Two. It's exactly 29/16 = 1 13/16, which is pretty close to two.
- 5050. Note that 1 + 100 = 2 + 99 = 3 + 98, etc, = 101. That's 50 of
them, since the last one is 50 + 51, so 101 * 50 = 5050. Those who had
infinite series' in school probably recognized the sum as n (n + 1) / 2,
which when you plug 100 in for n, gives exactly 101 * 50 = 5050.
- 6. The pattern 2,4,8,6,2,etc. continues on forever so all that's needed
is where 312 fits into the pattern. The pattern repeats with a frequency
of 4. 312 mod 4 = 0, which is the 6 in the pattern (same as 4, 8, 12, etc.).
I.e. 1sDigit(2
^{4}) = 1sDigit(2^{8}) = ... = 1sDigit(2^{312})
= 6.

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