By Scott Kim|Thursday, November 01, 2001

Garage Shuffle


Imagine that you are a valet parking cars in a garage. Each floor of this peculiar garage is a different size. Two types of cars are in fashion: sedans (shown as green 1-by-2 units in the above grids) and station wagons (blue 1-by-3 units). You need to park a given combination of cars on each floor, but you must leave yourself a clear path from each car door, shown as a black line, to the exit, shown as a gray line. Every car door must open into an empty square and must open from the driver's side; in all cases, the driver's side is on the left. The cars in grid A are properly parked. In B, however, there are no clear paths from two of the cars to the exit. And in C, one of the car doors is blocked. Can you figure out a way to park each set of cars?
1. Park three sedans and two station wagons in a 4-by-4 lot.
2. Park seven sedans and one station wagon in a 5-by-5 lot.
3. Park eight sedans and three station wagons in a 6-by-6 lot.
4. Park 12 sedans and three station wagons in a 7-by-7 lot.

Mileage Mystery

Driving to work one day, you glance at your dashboard and notice something interesting about your mileage indicators. Your odometer, which shows the miles driven since the car was manufactured, has hit 12,345.6 miles, and your trip meter reads 123.4 miles.

1. [Easy] When you bought the car, the odometer read 00,000.0, but due to a factory anomaly, there was mileage on the trip meter. You have never reset the trip meter. What did the trip meter read when you bought the car?

2. [Medium] The meter matches the first four digits on the odometer. How far must you drive--forward only--before this happens again?

3. [Very hard] What is the shortest distance you can drive before all 10 places of the two meters show all 10 digits, 0 through 9? An easier question: What's the answer if you can reset the trip meter to 000.0 at any time?

4. [Medium] Suppose you drive 2 billion miles in a car that started with an odometer reading of 000,000,000.0 (the odometer will zero out two more times). The odometer reading will contain all the digits 0 through 9 many times during this trip. What is the longest distance you can drive before all 10 digits appear on the odometer at one time?

A-maze-ing Bumper Cars

One green car and one blue car sit in the maze at right. If you press any of the four arrows on the control box, both cars move one square in the chosen direction. If one car hits a wall, that car does not move, but the other car will still move as long as nothing is in its way. If one car hits the other car, and that car is blocked by a wall, neither car moves. If a car drives into a brown square, the game is over. There are two exits, one green and one blue, at the top of the maze.

1. [Easy] Maneuver both cars out of either exit in the fewest possible moves. Note: Once a car leaves the maze, it may not reenter.

2. [Medium] Maneuver both cars out both exits simultaneously in the fewest possible moves.

3. [Harder] Maneuver both cars simultaneously through the exits of the same color in the fewest possible moves.


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© Copyright 2001 The Walt Disney
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