2C Problem-Solving Guidelines and Hints

four step process:

1. understand the problem
2. devise strategy for solving problem
3. carry out strategy and revise if necessary
4. look back to check, interpret and explain result

Traffic counters:

thin black tube stretched across the highway with "brain box" on the side to count the number of wheel sets that rolled over the tube.
41  counts of wheel sets. Find all possible combinations of 2 and 3 axle vehicles that could have gone over the tube.
41 = 2 x + 3 y, y odd

 x 19 16 13 10 7 4 1 y 1 3 5 7 9 11 13 sum 2x19 + 1x3 2x16+ 3x3 2x13 + 3x5 2x10 + 3x7 2x7 + 3x9 2x4 + 3x11 2x1 + 3x13

The cars and the canary:

two cars, 150 miles apart, begin driving toward each other on a long straight highway. one car travels 60 miles per hour, the other travels 100 miles per hour. A canary, starting on one car, flies back and forth between the two cars with instantaneous turnaround, when it meets the other car. If the canary flies 120 miles per hour how far does the canary fly, before the cars collide?

Mixing marbles:

2 piles of marbles each with 15 marbles, one black pile, one white pile.
Transfer 3 black marbles to the white pile
Then transfer ANY three marbles from the "white" pile to the black pile.
Show that if you now have k white marbles in the black pile, you have k black marbles in the white pile.

Coffee and milk example

Chinas one son policy:

• if the child is a son, no further children
• if the child is a daughter can have another child

suppose 10,000 families have children according to this policy and male and female children are equally likely, what is the average number of children per family and what is the demographics of the children?

 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th Boys 5,000 2,500 1,250 625 312 156 78 39 19 9 4 2 1 Girls 5,000 2,500 1,250 625 312 156 78 39 19 9 4 2 1

Total number of children: around 20,000 (19,990), half boys, half girls.

Puzzlers:

·        It takes 30 seconds to walk from the first(ground) floor of a building to the third floor. How long will it take to walk from the first floor to the 6th floor (same pace, same height between the floors)?

·        There are 3 kinds of apples all mixed up in a basket. How many apples must you draw without looking from the basket to be sure of getting at least two of one kind?

·        “ I am the brother of the blind fiddler, but brothers I have none”. How can this be?

·        Three boxes of fruit are labeled Apples, Oranges and Apples and Oranges. Each label is wrong. By selecting just one fruit from just one box you can determine the correct labeling of the boxes?

·         A man has to ferry a wolf, a sheep and a cabbage across a river in a boat, that just fits 2 things: the man and something else. If left alone the wolf will eat the sheep and the sheep will eat the cabbage. How can the man ferry them across the river?

 left side river right side Wolf, cabbage sheep -> wolf cabbage -> sheep wolf <- sheep cabbage sheep Wolf -> cabbage Sheep -> cabbage, wolf

·        A 150 foot rope is suspended at it two ends from the tops of 2 100 foot flagpoles. The lowest point of the rope is 25 feet from the ground what is the distance of the flagpoles?

·        Three prisoners know that the jailer has three white hats and two red hats. The jailer gives one hat to each prisoner and says, “ If you can deduce the color of your own hat, you will be freed.”  Each prisoner can see the hats of the other two prisoners but not his own. The first two prisoners say “ I cannot tell the color of my hat.”  The third prisoner is blind, but he is freed. What is the color of his hat?

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