Math Is Fun Forum

Nikkiman123

Member

Registered: 2010-10-28

Posts: 5

Sam Loyd Banana Puzzle...

Don't understand how to set up this problem to see the steps to the solution. Can anyone help?

How is it that when I buy yellow bananas at three shillings a bunch and the same number of red ones at four shillings a bunch I would get two more bunches for the same amount if I divided the money evenly between the yellow and the red bananas?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sam Loyd Banana Puzzle...

Hi

I think this is as good as you are going to do.

Bottom of the page.

http://www.mathsisfun.com/puzzles/sam-l … ution.html

My math solution is kind of complicated and some knowledge of congruences is required.

The problem forms 3 congruences. Let n be the amount of money.

The answers to the above congruences is the set:

Trying each one now will yield the answer. 0 of course is ridiculous.

168 gives 28 yellow and 21 red for 49 when we split the money and 56 when we do not so it is not right.

336 gives 56 yellow and 42 red for 98 when we split the money and 96 when we do not so it is the answer.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.