1. September 22, 2009 DRILL A: BOWLING PINS
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DRILL A: BOWLING PINS
Ten bowling pins form a triangular arrangement. Move 3 pins so that the resulting triangle points in the opposite direction.
DRILL B: CROSSING CLOCK HANDS On a regular clock, how many times will the minute hand and hour hand cross each other between the hours of 10 a.m. and 2 p.m.?

2. DRILL A: BOWLING PINS - SOLUTION
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DRILL A: BOWLING PINS - SOLUTION
Ten bowling pins form a triangular arrangement. Move 3 pins so that the resulting triangle points in the opposite direction.

3. DRILL B: CROSSING CLOCK HANDS - SOLUTION
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DRILL B: CROSSING CLOCK HANDS - SOLUTION
On a regular clock, how many times will the minute hand and hour hand cross each other between the hours of 10 a.m. and 2 p.m.?
1. Between 10:54 and 10:55 a.m.
2. At 12:00 noon
3. Between 1:05 and 1:06 p.m.

4. PROBLEM #4(OBSCURED BLOCKS): HOMEWORK SOL’N
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PROBLEM #4(OBSCURED BLOCKS): HOMEWORK SOL’N
Given a stack of individual blocks as shown. If all of the visible blocks were to disappear suddenly, how many blocks would remain? Write down your answer.

5. PROBLEM #4 : HOMEWORK SOLUTION (MODEL)
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PROBLEM #4 : HOMEWORK SOLUTION (MODEL)
= 17
There are 17 blocks left.

6. PROBLEM #5 (CROSSING PATHS) : HOMEWORK SOL’N
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PROBLEM #5 (CROSSING PATHS) : HOMEWORK SOL’N
Draw the following figure in one continuous action without lifting your pencil off the paper and without crossing any lines. You may begin at any point.

7. PROBLEM #1 (COUNTERFEIT GOLD COIN):
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PROBLEM #1 (COUNTERFEIT GOLD COIN):
A man is given 9 gold coins, but one of them is counterfeit and weighs less than the others. The man wants to determine which of the coins is counterfeit by using his balance scale. How can the man determine the false coin with only two uses of the balance scale? Write down your answer.

8. PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Divide the 9 gold coins into three equal groups of 3 coins each. Call them A, B, and C.
A B C
Place A and B on each side of the balance. Leave C on the table.
This is the first use of
the balance.

9. PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Did A and B balance?
YES NO
The light coin is in group C.
Discard the heavy group Keep the light group.
One light group has been identified with one weighing. Next, we determine which of those 3 coins is lightest.

10. PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Divide the 3 gold coins into three equal groups of 1 coin each. Call them D, E, and F.
D E F
Place D and E on each side of the balance. Leave F on the table.
This is the second use of
the balance.

11. PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
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PROBLEM #1 COUNTERFEIT GOLD COIN FLOWCHART SOLUTION:
Did D and E balance?
YES NO
The counterfeit coin is F.
The lighter coin is counterfeit.
In summary, the first weighing eliminated 2 groups of 3 coins each. The second weighing eliminated 2 of the last 3 coins.

12. PROBLEM #2 (AVERAGE SPEED):
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PROBLEM #2 (AVERAGE SPEED):
A train travels up a steep hill at a constant speed of 25 miles per hour. It takes one hour to reach the top of the hill. Neglecting the very small time it takes to turn around, how fast would the train have to travel down the hill in order for the average speed to be 50 mph for the entire round-trip?

13. PROBLEM #2 (AVERAGE SPEED): SOLUTION
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PROBLEM #2 (AVERAGE SPEED): SOLUTION
The train traveled 25 mph for one hour to reach the top of the hill. Average speed is equal to total distance divided by total time. 25 miles divided by 1 hour is 25 mph. Therefore, the train traveled 25 miles to reach the top of the hill in 1 hour.
The return trip down the hill is also 25 miles. Therefore, the total round-trip will be 50 miles. For the average speed to be 50 mph for the round-trip, the train must travel 50 miles in one hour, but the train already used up that hour on the trip up the hill. Therefore, it is impossible for the train to average 50 mph for the trip.

14. PROBLEM #3: HOMEWORK (PENTAGON SYMBOLS):
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PROBLEM #3: HOMEWORK (PENTAGON SYMBOLS):
This pentagon is divided into 5 equal parts. By coloring in one or more parts, how many unique patterns can you form? [A pattern is not unique if it can be achieved by rotating another pattern or if it is a mirror image of another pattern. Use only one color.]

15. PROBLEM #4: HOMEWORK (BLOCKED UP):
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PROBLEM #4: HOMEWORK (BLOCKED UP):
Arrange the blocks into three equal columns so that the sum of the numerals on the blocks is the same for each of the three columns.

16. PROBLEM #5: HOMEWORK (POWER PLANT LOCATION)
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PROBLEM #5: HOMEWORK (POWER PLANT LOCATION)
Constellation Energy will build a nuclear power plant along the Susquehanna River to provide electricity to city A and city B. They are located on the same side of the river, but at two different distances. The river is used to provide cooling water and the power plant must border the river. At what location along the river should the power plant be located so that the TOTAL LENGTH of power line connecting the two cities to the power plant is MINIMIZED?

17. September 22, 2009 HOMEWORK: (Problem Solving)
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HOMEWORK: (Problem Solving)
Complete any problems from today’s lesson that you didn’t already finish.
Answer problems #3 (Pentagon Symbols), #4 (Blocked Up) and #5 (Power Plant Location) on the printed sheet.