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## Main Question or Discussion Point

A farmer had a whole mess of chickens and ducks. He had twice as many ducks as he had chickens. One day he went to market and sold 413 of his ducks. When he came back home, he discovered that 19 of chickens had died. He now had half as many ducks as chickens.

The challenge is to find a solution without using algebra. Furthermore, a solution that would be accessible to an extremely talented 4th grader, but, with only a fouth grade education.

I do not know if such a solution exists. I'll outline my "best shot" in a subsequent post. It uses no algebra, but it uses too many things that might be viewed as "tricks" by a talented fourth grader. This means that it does a poor job of statifying the "accessible to a fourth grader" criteria. Another way of stating the problem is to find a solution that might be more accessible to a fourth grader than mine.

The problem was allegedly assigned to the son of a member in my church. He posed the problem to a group of about 10 adults in the church who could not solve it (without algebra). I was home sick that day. My wife bought the problem home and I got it, but, it took me quite a while.

I was not sure where to post this problem. I considered the "number theory" thread. Because of its similarity to the "three sailors, one monkey and a whole bunch of coconuts" problem that is described in the book "Algebra" by Saunders and MacLane. I considered other forums. This one seemed the most likely to have readers interested in this kind of thing.

I'll wait a while before I post my solutions. Maybe some of you will better me first and I won't have to.

I don't know how to use hidden text. What is the sequence of symbols that I type to get it started?

DJ

The challenge is to find a solution without using algebra. Furthermore, a solution that would be accessible to an extremely talented 4th grader, but, with only a fouth grade education.

I do not know if such a solution exists. I'll outline my "best shot" in a subsequent post. It uses no algebra, but it uses too many things that might be viewed as "tricks" by a talented fourth grader. This means that it does a poor job of statifying the "accessible to a fourth grader" criteria. Another way of stating the problem is to find a solution that might be more accessible to a fourth grader than mine.

The problem was allegedly assigned to the son of a member in my church. He posed the problem to a group of about 10 adults in the church who could not solve it (without algebra). I was home sick that day. My wife bought the problem home and I got it, but, it took me quite a while.

I was not sure where to post this problem. I considered the "number theory" thread. Because of its similarity to the "three sailors, one monkey and a whole bunch of coconuts" problem that is described in the book "Algebra" by Saunders and MacLane. I considered other forums. This one seemed the most likely to have readers interested in this kind of thing.

I'll wait a while before I post my solutions. Maybe some of you will better me first and I won't have to.

I don't know how to use hidden text. What is the sequence of symbols that I type to get it started?

DJ