September 21, 2010 IOT POLY ENGINEERING I1-11 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.?

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 PROBLEM #4 : YESTERDAY’S WORKSHEET 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.

PROBLEM #4 : HOMEWORK SOLUTION (MODEL) IOT POLY ENGINEERING I = 17 There are 17 blocks left.

IOT POLY ENGINEERING I1-11 PROBLEM #5 : YESTERDAY’S WORKSHEET 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.

IOT POLY ENGINEERING I1-11 PROBLEM #5 (CROSSING PATHS) : 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.

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 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? PROBLEM #2 (AVERAGE SPEED):

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. IOT POLY ENGINEERING I1-11 PROBLEM #2 (AVERAGE SPEED): SOLUTION 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.

IOT POLY ENGINEERING I1-11 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.]

IOT POLY ENGINEERING I1-11 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.

IOT POLY ENGINEERING I1-11 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?

September 9, 2008 IOT POLY ENGINEERING I1-11 HOMEWORK: (Problem Solving) 1.Complete any problems from today’s lesson that you didn’t already finish. 2.Answer problems #3 (Pentagon Symbols), #4 (Blocked Up) and #5 (Power Plant Location) on the printed sheet.