Puzzle 173
What number comes next in this sequence:
1 · 4 · 11 · 20 · 31 · 44 · ?
Puzzle Copyright © Kevin Stone
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Hint
A tricky base 8 question.
Answer
61.
Each term is a square expressed in base eight, 7 2=49 = 61 in base 8.
Puzzle 174
What number comes next in this sequence:
1 · 4 · 1 · 5 · 9 · 2 · ?
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Hint
The full sequence starts with 3.
Answer
6.
These are the decimal places of π ≈ 3.1415926.
Puzzle 175
What number comes next in this sequence:
1 · 8 · 9 · 64 · 25 · 216 · 49 · ?
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Hint
Think of squares and cubes.
Answer
512.
Each term alternates between a square and a cube, 8 3 = 512.
Puzzle 176
What number comes next in this sequence:
3 · 24 · 102 · 312 · 777 · ?
Puzzle Copyright © Kevin Stone
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Answer
1680.
This is n to the power of 5, starting with 2^5 = 32, with the last digit missing, 7^5 = 16807.
