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Workings

Hints
The first letters of the words are: E, S, P, C, I, A, P, A.

Answers
-----yee = employee -----egy = strategy -----igm = paradigm -----lse = convulse -----com = intercom -----bet = alphabet -----lel = parallel -----dee = attendee

Workings

Hint
How many hands did the first person shake?

Answer
190.

The first person shook hands with 19 others, the second had already shook hands with the first and therefore shook 18 hands, etc:

19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 190

Workings

Hint
Think of squares and cubes.

Answer
512.

Each term alternates between a square and a cube, 8 3 = 512.

Workings

Hint
Light travels over 186,000 miles each second.

Answer
Miles travelled by light in a second.

Reasoning
Light travels over 186,000 miles per second.

There are 2.54cm in an inch, 12 inches in a foot, 3 feet in a yard, and 1760 yards in a mile. So there are 2.54 x 12 x 3 x 1760 = 160,934.4cm in a mile.