### Brain Teasers

# Pen & Paper V

On a sheet of paper, write the following (incorrect) equation:

1 2 x 1 6 = 4 3 2

The challenge: Draw four lines, three on the left side of the equation and one on the right, to make the equation valid.

You cannot:

Change the = into a not-equal sign.

Manipulate the paper in any way.

Draw any curves.

Draw any dots or points.

1 2 x 1 6 = 4 3 2

The challenge: Draw four lines, three on the left side of the equation and one on the right, to make the equation valid.

You cannot:

Change the = into a not-equal sign.

Manipulate the paper in any way.

Draw any curves.

Draw any dots or points.

### Hint

Try to find a solution that does not involve the use of addition or subtraction.### Answer

On the right side of the equation, draw a diagonal line between the 4 and the 3, such that the right side of the equation is 4/32. On the left side of the equation, draw an identical line between the first 1 and the 2, and draw a small 7 to the upper-right of the 2.You should have:

1 / 2^7 x 1 6 = 4 / 3 2 (In this case, the ^ indicates that the 7 is an exponent.)

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## Comments

Possibly a simpler alternative would have been to make the 1/2 on the left, as you did, then draw a line over the whole expression on the left, and a "1" over the line.

Not sure I can effectively type this in here, but I'll try; you likely know what I mean. It leaves on the left:

1

____________________

1 / 2 * 16

And treat the right hand side exactly as you did: 4 / 32.

This is simpler as it evokes no exponents, and no newly constructed numerals.

Not sure I can effectively type this in here, but I'll try; you likely know what I mean. It leaves on the left:

1

____________________

1 / 2 * 16

And treat the right hand side exactly as you did: 4 / 32.

This is simpler as it evokes no exponents, and no newly constructed numerals.

I arrived at the same conclusion as described above.

Another possibility is: +2 x 1/16 = 4/32

in which the "+" is made by crossing the original initial "1" on the left side.

Good teaser!

Another possibility is: +2 x 1/16 = 4/32

in which the "+" is made by crossing the original initial "1" on the left side.

Good teaser!

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