FOR CHILDREN

PROBLEM # 1
The number 1961 has rotational symmetry because the number looks the same turned upside down. Find the next greatest number that has this unique feature.

FOR GROWNUPS

PROBLEM # 2
In the country of Math, the citizens pay numerically the same percent in income tax as they make in Math dollars per week. What is the maximum amount of money in Math dollars that a person can take home after paying taxes each week?

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SOLUTIONS TO PROBLEMS ON 08/25/05

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?

SOLUTION
 Hans - 59 kg, Simon - 73 kg, Josh - 78 kg.

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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