Trace: • springsummer2014
Table of Contents
Muddy Tracks
The image below shows tracks left by a bicycle riding on a muddy trail. Which direction was the bike traveling: left to right, or right to left? 1)
Bookworm
On a bookshelf is a two volume set. A bookwork eats his way through from the first page of Vol. 1 to the last page of Vol. 2. If each volume has 1cm of pages and each cover is 2mm thick, how far did the bookwork eat through? 2)
Grass
A man decides to do some landscaping at his home. He need to plant grass so he heads to the store. The salesman tells him about a new product that is very easy to use. You simply plant a small patch of this product, and each day it will double in size. The man asks how long it will take to fill his whole yard, and after some quick calculations the salesman tells him it will take 30 days. The man wants to done quicker than that, so he buys 2. How long will it take for his yard to be finished if he plants them both? 3)
Inheritance
Two ladies, Sue, Sandy, have each inherited some whole dollar sum of money. If Sue gives some amount of money to Sandy, they will have the same amount of money. If Sandy gives that same amount to Sue then Sue will have twice as much money as Sandy. If you remove the most significant digit from the amount of money that Sue has, and place it on the other end, that is equal to the amount of money that Sandy has. Each inherited less than 1 million dollars. How much money did each have? 4)
Fixing Buses
There a a 7 buses at a bus repair shop. The shop has 3 workers, all of equal skill. The time needed to repair each is is shown below (in minutes)
| Bus 1 | Bus 2 | Bus 3 | Bus 4 | Bus 5 | Bus 6 | Bus 7 |
|---|---|---|---|---|---|---|
| 12 | 17 | 8 | 18 | 23 | 30 | 14 |
How should the workers split up the work to fix all the buses in the minimum amount of time? How long will it take them? 5)
Matchstick Equation
On a table is an equation written in roman numerals with matchsticks.
XI + I = X
What is the fewest number of sticks you can move to make this equation valid? 6)
Numbers and Cards
In this game, three cards are placed in front of you face down. You are told that on each card is a number. No number is repeated. To play the game, you turn over one card at a time and look at the number. Each time you turn over a card, you must either declare the number on the card to be the largest of the three, or to reject that card. If a card is rejected, it can no longer be chosen. The object of the game is to choose the card with the largest number.
If you were to simply guess, you have a 1 in 3 chance of being correct. Is there a strategy that guarantees better odds? 7)
Palindromic Time
On a digital 12 hour clock, what is the shortest interval between two palindromes? Note: the clock does not display leading zeros: nine-thirty is displayed as 9:30, not 09:30. 8)
Gaokao Geometry
Strings and Holes
Suppose you have 10 strings. You also have a board with two rows of 10 holes. These holes lines up side-by-side as shown below.
The strings are arranged on the board following these rules: two strings cannot occupy the same hole, all holes must be filled, and each string must run across the board from one row to the other.
After the strings are arranged on the board, the number of crossings is counted. A crossing is any pair of strings that cross one another (see example below).
Considering all possible string arrangements, what will be the average number of crossings? 10)
Chess
Place 5 white queens and 3 black kings on a 5×5 chess board so that none of the kings are in check. 11)
Flipping Coins
Start with 7 coins, all laying heads up. For each round of flipping, you must flip 5 coins. What is the minimum number of rounds it take to have all coins showing tails? 12)
Cops
There are two cops on a one way street. They are determined to pull over anyone breaking the law. A taxi driver is going down the street the wrong direction, but the cops do not pull him over. Why not? 13)
Matchstick Triangles
Arrange nine matchsticks so that they form three equilateral triangles like the image below. By moving three sticks, can you form four equilateral triangles ? Sticks cannot be broken or overlapped. All nine sticks must be used. 14)
Odd Sum
Connect The Dots
Merciful Jailor
You are a prisoner awaiting execution. Your jailor comes to your cell the night before and tells you he will make a deal with you. He shows you two urns: one has 10 red disks and the other has 10 green disks. He tells you that in the morning he will choose a disk while blindfolded. He continues by saying that he will leave the urns and disks with you for the night, and you can choose how the disks are distributed between the two urns. If the disk he chooses is green, he will let you live. If he chooses a red disk, you will be executed. If the jailor takes off his blindfold and doesn't see the original 20 disks, you will be executed. He will continue searching for a disk until he finds one, so if an urn is empty he will pick a disk from the other urn.
If you leave the urns as they are, you have a 50% chance of the jailor choosing a green disk. Is there a way to rearrange the disks to improve your odds? What is the best probability you have of living? 17)
Dice Game
Two men, Ben and Jerry, are playing a dice game. The dice faces are colored either red or blue. To play the game, each player rolls two dice. If the colors on both of the dice are the same, Ben wins. If the colors are different, Jerry wins. One of the die has 5 red faces and 1 blue face. How should the second die be colored to ensure that both players have an equal chance of winning? 18)
Questions Asked
| Junming Diao | 3 |
| Jay Brady | 3 |
| Josh Sypherd | 3 |
| Dr. Jeffs | 3 |
| Richard Black | 3 |
| Dr. Warnick | 1 |
| Mitch Burnett | 1 |
| Mark Ruzindana | 1 |