# Bogglers Solutions

By Scott Kim|Thursday, November 01, 2001

Garage Shuffle

 There are multiple solutions to 2, 3, and 4. 1. 2. 3. 4.

Mileage Mystery

1. The trip meter turns over to zero every 1,000 miles, so the trip reading reflects 13,123.4 miles. 13,123.4 - 12,345.6 (the odometer reading) = 777.8.

2. After 1,010.1 miles, the odometer will read 13,355.7, and the trip meter will read 133.5.

3. After 861.1 miles, the readings will be 13,206.7 and 984.5. A mere .9 miles further it happens again (13,207.6 and 985.4). The best answer requires resetting the trip meter: Drive 6.6 miles, reset the meter, then drive 45.6 miles. The odometer will read 12,397.8, the trip meter 045.6. This is the smallest possible trip meter reading that doesn't contain 1, 2, or 3--the first three digits of the odometer.

4. The longest distance during which the odometer never shows all 10 digits is the 24,691,357.9 miles between 987,654,321.0 and 012,345,678.9 on the odometer. To prove this is the best answer, note that the odometer cannot contain all 10 digits if the first two digits are the same. The only time the first two digits roll over from one number with both digits the same to another such number is from 99 to 00. That means that for any other pair of consecutive two-digit numbers, say 39 to 40, there is at least one pair of odometer readings starting with those numbers that each contain all 10 digits, and the distance between those two readings must always be less than 20,000,000 miles.

A-maze-ing Bumper Cars

1.   11 moves: RUURUUULUUU
2.   19 moves: RUURUURDDLLULLUUURU
3.   21 moves: LUURURURRDDLLULLUUURU

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