FOR CHILDREN

PROBLEM # 1
Three boys, Josh, Hans, and Simon are sitting around on a farm with nothing to do. They walk into the barn and notice a scale used to weigh cattle. They decide to weigh themselves. Unfortunately, the scale begins at 100 kg. The problem is that none of them weigh more than 100 kg. They decide to weigh themselves in pairs. Josh was sure that he weighed the most.

Hans and Simon together = 132 kg.
Simon and Josh together = 151 kg.
Josh and Hans together = 137 kg.

What did they each weigh?

FOR GROWNUPS

PROBLEM # 2
The measure of angle ABC in triangle ABC in Figure 1 is 45 degrees. Point D lies on side BC such that the length of BD is one half the length of DC. If the measure of angle DAB is 15 degrees, determine the measure of angle ACB.

(note: the drawing is not drawn to scale and correct proportions)

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SOLUTIONS TO PROBLEMS ON 08/11/05

FOR CHILDREN

PROBLEM # 1
There are fewer than 6 dozen rocks in a collection.
Grouping the rocks by 2s leaves 1 extra.
Grouping them by 3s leaves 2 extra.
Grouping by 4s leaves 3 extra.
Grouping by 5s leaves 4 extra.

How many rocks are in the collection?

SOLUTION
59.

FOR GROWNUPS

PROBLEM # 2
What is the sum of 1 + 1/(2x3) + 1/(3x4) + 1/(4x5) + 1/(5x6) + .....?

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