Gus's Food Consumption

Gus Food Consumption Scenarios:

  • Tabby and Merlin fight, Gus eats 1/2 leaving 1/4 each for them.
  • Tabby and Merlin fight, Gus eats 1/3, leaving 1/3 each for them.
  • Tabby and Merlin fight, Gus eats 1/2 up front. Then each cat, including Gus, gets 1/3 of the rest.

Gus would get 1/2(3/6) + 1/3 of 1/2 (1/6) = 4/6 or 2/3. Tabby and Merlin would only get 1/6 each.

Which is the most likely scenario?

Gus is 18 lbs, Tabby 7 and Merlin 8. This means of the total cat weight, Gus represents 18/33, or 6/11, over half the total weight.
So his consumption should be reasonably close to this ratio. Use 11 units as a factor.

2/3 of 11 is 22/3 or 7 1/3. The most Gus can eat under any of the above scenarios is 7 1/3.
Gus however, is entitled to only 6 - given. 11/3 would mean only 2 2/3 each. it seems obvious that Gus eats more than that.
If greater consumption is needed to maintain his portly stature, Gus must eat proportionately to his weight.

Of course this assumes all else is equal.

Gus has "stagefright" and often flees from the kitchen if you catch him eating. I think he prefers to eat in the dark.

Tabby and Merlin have higher metabolisms and get much more exercise…

There are other possibilities:

Tabby gorges herself and pulls a bulemia stunt. This wastes half of the meal. If you don't clean it up immediately, Merlin will nibble at it. Yeah, it's pretty gross. It's not like Merlin is a baby bird you know.

So we end up with each getting 1/6. Unless there's a fight. Then take initial scenarios and divided by two.
This means Gus will at least get a 1/4. It's possible he get's 1/3. Merlin and Tabby could end up with only 1/12 each. This is 1/3 of their RDA. Really!

what is the probability that Paul is a math nerd?

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