We have been quite lucky with the weather recently, it has got steadily warmer each day over the last five days.
By this, I mean that the midday temperature rose by the same amount each day.
The average midday temperature was 2 °C, and I know that it was below freezing (0 °C) on two of the days.
I also know the product of the temperatures was over 500 but below 2,000 and each daily midday temperature was an integer.
What were the last 5 midday temperatures?
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Hint
What must the middle midday temperature be? Remember that the temperatures are in degrees Celsius.
Answer
The midday temperatures were -6, -2, 2, 6, 10 °C.
Each day the midday temperature increased by a steady 4 degrees.
Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).
Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).
If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.
If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does match all of the requirements.
If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.
Any larger increase makes the product even larger, so we can stop checking.
So the only possible answer is -6, -2, 2, 6, 10.
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