Trace: • fall2014
Table of Contents
Connect the Dots
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
. . . . . . . . . . . . . . . . . . . . . _ . . .
Go
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)
Weighing Coins
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)
2 Friends
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)
Transporting Apples
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)
Walking
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)
Sequence
Blue Eyes
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? 8)
Bottles
A vendor sells bottles of water for $1. You can also trade in two empty bottles and get a full bottle of water. If you start with $61, how many full bottles of water can you get? 9)
Can
A can manufacturer needs to build a can that will hold 1.5 liters. They want to be able to use as little material as possible. What should the dimensions of the can be? (remember that 1 mL = 1 cm3) 10)
Triple threat
This week's question was a best-of-three lightning round.
1 - Four matchsticks are arranged into a square. This configuration has four 90 degree angles. How can you rearrange these stick to give a configuration with 16 right angles?
2 - Two friends grab sodas out of the freezer at the store. One of the sodas is frozen, but the other isn't. How can this be?
3 - A couple goes on vacation. Two months after they come home, the wife calls the police to let them know they saw a dead body near the cabin they stayed in. The officer said they had just discovered this and they were investigating a murder. The officer said she was now a suspect and asked why she had waited so long to come forward. After she gave her explanation, the officer was satisfied and let her go. How did she explain the situation? 11)
Pirates
Five pirates raid the ship of a wealthy bureaucrat and steal his trunk of gold pieces. By the time they get the trunk aboard, dusk has fallen, so they agree to split the gold the next morning.
But the pirates are all very greedy. During the night one of the pirates decides to take some of the gold pieces for himself. He sneaks to the trunk and divides the gold pieces into five equal piles, with one gold piece left over. He puts the gold piece in his pile, hides it, puts the other four piles back in the trunk, and sneaks back to bed.
One by one, the remaining pirates do the same. They sneak to the trunk, divide the coins into five piles, with always one coin left over. Each pirate puts the gold coin in his own pile, hides it, and puts the remaining four piles back in the trunk.
What is the smallest number of coins there could have been in the trunk originally? 12)
Sticks
There are two sticks. Each stick will burn in 1 hr, but the rate at which it burns is unknown and non-uniform. How can you use these sticks to time 15 minutes? 13)
Camel Herders
2 camel herders (Jack and Bill) decide to sell their camels and buy some sheep. When they get to the market, they find out that the price to sell a camel is equal to the total number of camels in your herd when you arrive at the market. To increase their money, they decide to pool their camels into one big herd before they arrive, then sell them all. They take the money and buy sheep at $10 each. After they buy the sheep, they have some money left over and use all of it to buy one goat. It turns out that when they split the sheep into two equal herds, there is one extra sheep. Jack has the larger herd and tells Bill that he can have the goat. Bill says this is still not a fair split, so Jack takes one of his own dogs and gives it to Bill. Bill and Jack both agree that this is now a fair split. How much is one dog worth? 14)
Square Digits
Let N be some two-digit number, with the digits denoted as A and B. Let N2 be a three-digit number with the digits denoted as C, A and B.
N = AB N^2 = CAB
What digit does C represent? 15)
Questions Asked
| Junming Diao | 2 |
| Jay Brady | 1 |
| Josh Sypherd | 3 |
| Dr. Jeffs | 3 |
| Richard Black | 2 |
| Dr. Warnick | 1 |
| Wu Yifeng | 3 |