Bogglers Solution

By Scott Kim|Wednesday, December 03, 2003

MIRROR WORLDS

This question was first framed as a logic puzzle in Martin Gardner’s book The Ambidextrous Universe (Basic Books, 1964). It is also featured in William Poundstone’s How Would You Move Mount Fuji? (Little, Brown, 2003).

Does a mirror reverse left and right? It is more accurate to say that a mirror reverses the relative positions of points along a line perpendicular to, not parallel to, the mirror. For example, if you stand on a mirror that is lying flat on the floor, the mirror reverses the relative positions of your feet and head, which are nearer and farther from the mirror. Why then do we say that a mirror reverses left and right? We say this because our bodies are bilaterally symmetrical. When you stand in front of a wall mirror and hold up your right hand, your reflection seems to hold up its left hand, so we say a mirror reverses left and right. But you could say it reverses front and back: Imagine walking straight forward into your reflection, matching head to head, feet to feet, hands to hands, and heart to heart. Everything fits, but your front and back are reversed. So you could say, although it’s less intuitive, that a mirror reverses top and bottom, or front and back. 

1. Balls fall down because “down” is defined by the direction of gravity, which exerts a downward pull on objects.

2. Clock hands turn clockwise because “clockwise” is defined by the direction in which the hands of a clock move.

3. The letters of the alphabet are in alphabetical order because “alphabetical order” is defined by the order of the letters in the alphabet.

4. A concave curved mirror, such as a bent piece of shiny metal, or two mirrors that meet at a right angle, such as at the corner of a room.

5. A horizontal mirror on the floor or ceiling.

6. A vertical mirror hanging on the wall.

MIRROR OBJECTS

These items were selected from Anything Left-Handed (www.anythingleft-handed.co.uk).

Baseball glove: Fits the right hand instead of the left.

Corkscrew: Spirals counterclockwise to fit the twisting direction more natural for a left hand.

Camera: Shutter button and main controls are under the left index finger.

Watch: Winding stem is on the left instead of the right; the watch is worn on the right wrist.

Playing cards: Numbers appear in all four corners, not just the upper left and lower right.

Tape measure: Numbers are printed on the other edge, running right to left, so they read correctly when the tape is held with the right hand and the body is pulled with the left.

Address book: Opens on the left; the tabs are reversed for selection with the left thumb.

Serrated bread knife: A right-handed knife often has serrations on the left edge of the blade to correct for the hand’s natural twisting action. A left-handed knife has serrations on the right.

Pencil: Pencils themselves are ambidextrous, but the words printed on the shaft are biased. A left-handed pencil has words printed in the other direction.

Fountain pen: Has a smooth rounded ball at the end of the nib, which allows ink to flow smoothly from almost any angle. Many conventional nibs will dig or sputter if they are pushed in the wrong direction.

Golf clubs are the most popular left-handed items on eBay. Guitars are also popular. Scissors, possibly the most common left-handed item, are not profitable enough to sell on eBay.

MIRROR WORDS

HOT

ECHO

ATOM

DIOXIDE

TATTOO

OBOE

TOMATO

OXHIDE

EBBED

The first letters spell the phrase “head to toe.”

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