Monthly Archives: December 2011

Change for a Dollar

How many ways are there to make change for a dollar? Source: Julia Robinson Mathematics Festival SOLUTION One easy and quick way is to┬ápay four quarters or ten dimes. But, things get complicated pretty fast if we mix pennies, nickels, … Continue reading

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Nine Llamas

A zoo keeper houses 9 llamas all together in a large square cage. Strangely, all these llamas are very lethargic and remain in the position shown in the figure below at all times. Can you give each its own private … Continue reading

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Dividing Right-Angled Figure

Dividing Right-Angled Figure Divide the rectilinear right-angled figure shown below into two equal areas with one straight line . Source: Julia Robinson Mathematics Festival SOLUTION Area of right-angled figure = area of rectangle + area of square We want the … Continue reading

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Dividing Land

A man leaves a piece of land (see below) to his four sons, with instructions that it should be divided up into 4 equal pieces, each having the same shape as the original piece of land. How can this be … Continue reading

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Regular Pentagram

Find the area of the shaded region as a fraction of the area of the entire regular pentagram. Source: Julia Robinson Mathematics Festival SOLUTION Congruent Triangles Triangles 1 through 6 are congruent to each other. Triangle 7 is congruent to … Continue reading

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Triangle 70

The perimeter of a right triangle is units. The sum of the squares of the three sides of the right triangle is . Find the length of all three sides of this right triangle. Source: mathcontest.olemiss.edu 12/5/2011 SOLUTION We are … Continue reading

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Eighty-Five Four Digit Numbers

How many four digit numbers contain the digit pattern at least once and only once? Source: mathcontest.olemiss.edu 11/12/2007 SOLUTION Case 1: Nine choices for because we do not want 8585. There are 9 numbers. Case 2: Not 8 means nine … Continue reading

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Inscribed Triangle

Prove that the total area of the regions 1 and 2 below equals the area of the triangle. Regions 3 and 4 are parts of the semi-circle in which the triangle is inscribed, and and are diameters for the other … Continue reading

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