Radio Astronomy Systems Research Group

Can you connect all of the dots in the grid below following these rules: ¹⁾

1. You have to connect all the dots with a continuous line (no pencil lifts)

2. You can't cross a line or use diagonals

3. The underscore is a space that you cannot go through

. . . . .
. . . . .
. . . . .
. . . . .
. _ . . .

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Start with 4 white and 4 black stones in the order shown.

The goal is to have the stones alternate after only 4 moves:

Here are the rules for each move:

1. You must move two stones at a time.

2. Only adjacent stones may be moved.

3. Stones are only adjacent if the is no space between them

3. You must leave spaces if you create them. ²⁾

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There are five boxes filled with coins. All the coins look and feel identical. However, the coins in four of the boxes weight 10 grams each, while the coins in the fifth box weigh 11 grams each. You have a scale and can weigh any combination of coins. How can you determine which box holds the heavier coins in only a single weighing? ³⁾

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Two friends, Jack and Bill meet each other one day. They haven't seen each other in a long time. Jack asks Bill how he is doing. He replies that he has three kids. When Jack asks how old they are, Bill tells him that the product of their ages is 72 and the sum of their ages is the same as Jack's birthday. Jack says that isn't quite enough information, so Bill tells him that his oldest child just started taking piano lessons.

How old are Bill's children? ⁴⁾

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A farmer has 3000 apples to deliver to a city 1000 miles away. His truck can only carry 1000 apples at a time. There is only one road he can travel on, and it has a 1 apple per mile toll. He only has to pay this toll if he is traveling toward the city; if he is traveling toward his home he does not need to pay a toll. If he wants to, he can leave piles of apples at any point along the road and come pick them up later. How many apples can he deliver to the city? ⁵⁾

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A man starts walking from point A. He walks south 1 mile, then west 1 mile, then north 1 mile. He ends up back at point A. What are all the possible locations for point A? ⁶⁾

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1
1 1
2 1
1 2 1 1
?

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In the middle of teaching a class, Dr. Jeffs calls up two students to the board to work a problem. He notices that the two students he randomly chose both happen to have blue eyes. If you know that the probability of choosing two students with blue eyes is .5, what is the total number of students in the class? ⁷⁾

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