Brain Teasers
The Dishonest Grocer
Quinn, Ralph, and Steve work at a grocery store that sells apples, bananas, and oranges. Quinn says, "Seven apples and five bananas cost the same as six oranges." Ralph says, "Four apples and nine oranges cost the same as five bananas." Steve says, "Six oranges and three bananas cost the same as four apples." Only one is lying...but who?
Hint
The three values equivalents must be considered in pairs. The one false equivalent leads to two impossible situations, while the pair of true equivalents is a possible situation.Answer
Quinn is lying.Let a equal the price of apples, b equal the price of bananas, and o equal the price of oranges. Quinn is saying that 7a + 5b = 6o. Ralph is saying that 4a + 9o = 5b. Steve is saying that 6o + 3b = 4a.
Combining Quinn's and Ralph's statements, we get 11a = -3o. This is impossible.
Combining Ralph's and Steve's statements, we get 15o = 2b. This is possible.
Combining Quinn's and Steve's statements, we get 8b = -3a. This is impossible.
This means that either Quinn is lying, or Ralph and Steve are both lying. But there only can be one liar: obviously Quinn.
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Comments
Very nice teaser. Original twist on some standard themes. I would put this in the logic bin because there is no need for a calculator, but putting it in the math category almost serves as misdirection. The only real math is recognizing that the sum of positives can't be negative.
I started out setting up a system of equations, but realized that there were like terms I could substitute directly. That made life easier.
Again, great teaser. I found it quite original (to me).
I started out setting up a system of equations, but realized that there were like terms I could substitute directly. That made life easier.
Again, great teaser. I found it quite original (to me).
Nice teaser. I really liked it - but my 2 favorite topics are math and logic. And with my background in these 2 areas, I found it relatively simple to solve.
A scip model for solving this teaser can be found at
https://gist.github.com/saska-gist/
d766963f9af923aa25f20240f3cc8374
https://gist.github.com/saska-gist/
d766963f9af923aa25f20240f3cc8374
This was one of the best teasers I've seen in a long time, if not ever. Great one!!!
Very happy to see this as a Teaser of the Day!
This was a great way to test your logic and math skills - I loved it!
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