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The Delivery Dilemma

The local pizza joint delivered pizza and subs. Three employees were hired to deliver: John, Heather, and Luigi.

Based on the following statements:

  1. If John delivered pizza, then Heather delivered subs.
  2. If John delivered subs, then Luigi delivered pizza.
  3. If Heather delivered pizza, then Luigi delivered subs.

Which person or persons can we be sure always delivered the same food, and what food was it?

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The answer is

Heather always delivered subs.

And we can figure this out by

changing the third statement to its contrapositive, which is equivalent: "If Luigi did not deliver subs, then Heather did not deliver pizza." In other words, "If Luigi delivered pizza, then Heather delivered subs."

Now the statements we have are:

(1): If John delivered pizza, then Heather delivered subs.

(2+3): If John delivered subs, then Luigi delivered pizza. If Luigi delivered Pizza, then Heather delivered subs.

Either way, Heather must deliver subs.

What about the others?

Based on the above reorganizing of the statements, John can have delivered either item and there is a valid configuration. If John delivers pizza, then Luigi can deliver either item. So the only person whose item is fixed is Heather.

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    $\begingroup$ rot13(Guvf fbyhgvba pna nyfb or ernpurq ol nffhzvat gung Urngure qryvirerq cvmmn. Vs fb, gura Yhvtv zhfg qryvire fhof. Ohg gura, ol fgngrzrag 2, Wbua zhfg unir qryvirerq cvmmn. Ohg gura Urngure jbhyq unir qryvirerq fhof ol fgngrzrag 1. Guvf vf n pbagenqvpgvba, fb guhf Urngure zhfg qryvire fhof.) $\endgroup$ – Cloudy7 Apr 15 at 23:17
  • $\begingroup$ This is incorrect. It's possible that Luigi delivered both foods, John delivered only subs, and Heather delivered only pizza. (And don't say the puzzle implies each person delivered only one type of food. Its asking "Which person or persons can we be sure always delivered the same food" implies that it's possible that someone did not always deliver the same food, i.e. delivered both types.) $\endgroup$ – msh210 Apr 17 at 0:09
  • $\begingroup$ @msh210 The "the" in that sentence seems to imply that each person delivers exactly 1 food. And the "always" appears to me to be "in every potential case", as it is commonly used in mathematics: e.g. "If you have an odd number and square it, you always get another odd number". I agree that if you drop the "one food" assumption, you get nobody being constant across all cases, but the "it" at the end of the question implies that we do need to find at least one person who always delivers the same thing. $\endgroup$ – Deusovi Apr 17 at 1:59

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