Intro to Hole Punching | DAT

What are Hole Punching Problems?
 A square sheet of paper will be
folded 2-3 times
 You will be shown the paper
after each fold
o Dashed lines represent
the original outline of the
paper
o Solid lines represent the
paper’s folded edges
 The last fold will be pictured
twice
o In the latter, one or more
holes will be punched
through the paper
Sample Fold
In this fold, we will fold the left corner (red
arrow) over to the right corner (blue arrow).

Sample Folds
The paper will be folded 2-3 times. The final
state of the paper will be pictured twice with one
or more holes punched through the paper.

Suppose we were going to
perform the following fold:
Theoretically, we could fold the
left corner up our of the page or
down into the page
(a)
(b)
Folding In and Out of the Page
The above fold could be carried out by folding
(a) out of the page, or (b) into the page. In this
section, all folds are made out of the page, so (b)
would not be possible.
You are tasked with identifying
the locations of all holes in the
paper after it is unfolded

There are 4 types of possible
diagonal folds:
Rules
 At no time may any part of the
paper leave the boundaries of the
original square
The 4 Diagonal Folds

An Illegal Fold
This fold would be disallowed because the paper
extends beyond the perimeter of the original
sheet of paper (red).

There are 4 types of possible
horizontal/vertical folds:
Folds must be made out of the
page
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© 2017 J Co Review, Inc., Accessed by Guest on 07-31-2017
Intro to Hole Punching | DAT
Start and End Points
During the transition from state (b) to (c) in the
previous diagram, the upper left corner (red
arrow) will be folded down to the lower right
corner (blue arrow).
The 4 Horizontal/Vertical Folds

Note that any of the pictured
folds may be rotated 90°, 180°,
or 270°
o This can change
horizontal folds to
vertical folds

With those start and end points
identified, we draw a line
between them
Discerning the Fold Type

Although there are only a few
fold types, it becomes difficult to
discern the fold type after it’s
been compounded with other
folds
Connecting the Start and End Points

The fold axis will be the line
that’s:
o Perpendicular
o Equidistant between the
start/end points
(a)
(b)
(c)
Compounding Folds
The fold in (a) is easily diagnosed as a half-page
diagonal fold. But after folds become
compounded on top of one another, the fold
types become trickier to discern. For instance, it
isn’t immediately apparent what type of fold
brings us from (b) to (c).


The Fold Axis
The fold axis is the line perpendicular to the line
connecting the previously identified start and end
points, and equidistant between those 2 points.
To identify the fold type, we
deduce its axis
Start by choosing a point on the
paper prior to the fold, and
identifying where it will end up
after the fold

Once we’ve identified the fold
axis, we can see that the fold
does conform to one of the fold
types we’ve previously
introduced
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© 2017 J Co Review, Inc., Accessed by Guest on 07-31-2017
Intro to Hole Punching | DAT

o It’s a half page, diagonal
fold
The newly-formed crease will lie
on the fold axis
Half Hole
Half holes may appear when a hole straddles the
edge of a crease.
Answer Choices
 Each answer choice will contain
a grid of 16 circles
o Shaded circles indicate
locations where a hole
exists
The Fold Crease
The new fold crease (pink) sits on the fold axis
we’ve identified (green).
The Holes
 Holes may be punched in any of
the 16 boxes in the following
grid:
Sample Answer Choice
Shaded circles indicate the locations of punched
holes.
Possible Hole Locations
There are 16 possible locations where a hole may
be punched.



A hole will always be entirely
contained within one of those 16
cells
o It’ll never span 2 or more
cells
Usually only one hole is
punched, but it’s possible to see
multiple holes
o Problems with multiple
holes generally have
fewer folds
Half holes are also possible
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© 2017 J Co Review, Inc., Accessed by Guest on 07-31-2017