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Answer:
The temperatures were 6, 2, 2, 6, 10 °C.
Each day increased by a steady 4 degrees.
As the temperature rose steadily each day and the average was 2 degrees, we know the middle temperature was 2 degrees.
If we assume a daily increase of 1, the sequence would be 0, 1, 2, 3, 4. This doesn't work we require 2 negative temperatures.
If we assume a daily increase of 2, the sequence would be 2, 0, 2, 4, 6. This doesn't work we require 2 negative temperatures.
If we assume a daily increase of 3, the sequence would be 4, 1, 2, 5, 8. This doesn't work as the product is less than 500.
If we assume a daily increase of 4, the sequence would be 6, 2, 2, 6, 10. This matches all of the requirements.
If we assume a daily increase of 5, the sequence would be 8, 3, 2, 7, 12. This doesn't work as the product is more than 2000.
So the only possible answer is 6, 2, 2, 6, 10.
Puzzle 416
My 10, 8, 3 is a boisterous lad.
My 9, 4, 8, 7 is the underground part of a tree.
My 6, 5, 7 is admired by some.
My 3, 4, 1, 7 can be used to keep a door shut.
My 2, 1, 7, 6, 9 is where we pray.
My whole is where some discoveries are made.
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