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The rules for exhaustion from starvation are given in the basic rules (and PHB) as:
A character needs one pound of food per day and can make food last longer by subsisting on half rations. Eating half a pound of food in a day counts as half a day without food.
A character can go without food for a number of days equal to 3 + his or her Constitution modifier (minimum 1). At the end of each day beyond that limit, a character automatically suffers one level of exhaustion. A normal day of eating resets the count of days without food to zero.
The second paragraph strikes me as odd, because it seems to imply that a creature with a reasonable Constitution modifier can make their rations last longer by alternately starving themselves for several days and then eating a full day's rations.1 Perhaps there are more elaborate strategies that might last even longer.
So, given the above rules and assuming I have a Constitution modifier of +0, what is the longest I can go on 10 days' rations without taking a level of exhaustion from lack of food, and what is the rationing strategy to achieve this? Assume that I have no other food source besides these rations, but my other needs (e.g. thirst) are taken care of, so making these rations last is my only concern.
1 On the other hand, maybe this isn't so odd, given that in real life, humans are evolved for survival in conditions of alternating feast and famine.