# Create a 1 inch measurement

This is a follow up to the "Create a 3 inch measurement" puzzle, which got a lot of innovative solutions. Using the standard 8.5 x 11 inch paper, can you create a 1 inch measurement only by folding? Again no marking allowed. No ruler either.

One more thing. I realize that folding the 8.5 inch side three times can get you 1.06 inches. But can you do better than that? Maybe I was overdoing it, but I think I got it in more than 3 folds.

• new stack proposal: Paper Folding Golf SE. :) – Rubio Feb 23 '17 at 22:47

A solution in 4 folds:

1. Fold one corner down to the opposite side. We now have a triangle that is 8.5" by 8.5", and a flap below it that is 2.5" by 8".
2. Fold the flap up, and call this Flap A. Now unfold the paper and turn it upside down.
3-4. Repeat the same steps to get a Flap B.
Now, unfold the paper and just fold down Flap A and Flap B. the thin space between the two flaps should have length exactly 1".

This is because

The flaps are of length 2.5", and when folded up (or down) that is another 2.5" for a total of 5". If Flap A accounts for 5" and Flap B accounts for another 5" from either side of the 11" length of the paper, the space in between should be 1".

A solution in 3 folds:

1. Fold diagonally to get triangle of side length 8.5, leaving 2.5 inches on the 11 inch side uncovered
2. Fold the 2.5 inch flap up, leaving 6 inches on the 11 inch side uncovered
3. Create a fold at the 6 inch mark on the 11 inch side using the covered part
Unfold the 2.5 inch fold in order to get a flap of 5 inches which leaves only 1 inch uncovered on the 11 inch side.

• This is an easier, more accurate way of finding a point one inch from the end of the 11" side than I used in my ruler answer to the previous question. As discussed in my ruler answer, another nine pinches allow creating a ruler with one pinch every inch. – Jasper Feb 24 '17 at 5:28

This answer uses the first six steps from my ruler answer to the previous question. (LliwTelracs' answer is a better way of finding the same point.)

The labels are optional; they serve only to uniquely identify the points and creases. Label the ends of a short side NW and NE.
Label the corresponding ends of the other short side SW and SE.
Clockwise from the top right, the points are NE, SE, SW, and NW.
1. Crease between NW and SE. Unfold.
2. Pinch a mark halfway between NE and SE. This mark is point $1/2$.
3. Crease between SW and $1/2$. Unfold. Where this crease crosses NW-SE is point $1/3$.
4. Fold the raw edge SW-SE to lie on point $1/3$, such that raw corner SW lies along the NW-SW raw edge, and raw corner SE lies along the NE-SE raw edge. Pinch a mark at the NE-SE raw edge end of the fold. Unfold. This mark is point $1/6$.
5. Fold the raw edge SW-SE so that point SE lies on point $1/6$, and point SW lies along the NW-SW raw edge. Pinch a mark where the NW-SE crease crosses the new fold. Unfold. This mark is point $1/12$.
6. Crease from point SW through point $1/12$ to raw edge NE-SE. Unfold. The NE-SE end of this crease is point $1/11$.

With another 9 pinches, it is possible to turn the 11" side of the paper into a ruler with one pinch every inch.

Only 2, but if you want to "mark it on side", you need 3.

It's not exactly 1, but something like 1.01077, because it's possible that Wolfram|Alpha rounded it somewhere.
Edit: According to other posts - this is only 2 folds.

• What are the references for the creases? – Jasper Feb 24 '17 at 20:20