Trace: • springsummer2014
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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.
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? 11)
Questions Asked
| Junming Diao | 3 |
| Dr. Jeffs | 2 |
| Josh Sypherd | 2 |
| Jay Brady | 3 |
| Richard Black | 1 |