Paper folding / cutting

1. Ye topic hai kya?

Asli kagaz: fold, ched ya kaat, phir kholo. Picture ka water/mirror nahi (Water image, Shapes / mirror). Cube ki faces nahi (Dice / cube).

Do sawaal

Punch: gol ched — kitne, kahan. Cut: kone/edge se tukda — kholne par kaun si shape.

Pehle lock

Har fold ek mirror line. Jo punch fold pe nahi, wo us line ke doosri taraf copy. Aakhri fold punch ke sabse kareeb — usi crease se pehle copy socho, phir purane folds.

2. Punch — parat se gino

Half-fold: har baar parat double. Punch tabhi har parat mein tab jab kisi crease pe na lage.

Folds (half)	Parat	Punch fold pe nahi	Punch 1 fold pe	Punch 2 folds ke crossing pe
1	2	2	1	—
2	4	4	2	1 (original ka centre)
3	8	8	4	2

Punch kisi fold pe nahi → ched = 2^n
Punch exactly k creases pe (unka milna) → ched = 2^(n−k)

“4 parat isliye 4 ched” tabhi jab punch crease pe na ho. Centre (dono folds ka kone) pe punch = 1 ched beech mein.

Example yahan horizontal fold — neeche ki half upar (vertical-fold wala example Shapes page pe hai, yahan nahi).

1. Open dash = agla fold

2. Folded + punch packet = upar half; punch left, fold pe nahi

3. Kholo 2 ched, same left, upar+neeche

3. Kaat — tukda nikaalo

Punch gol gaddha hai. Cut = scissors se kone/edge ka tukda. Unfold par wo tukda har copy pe dikhega.

Fold-edge (crease) se andar kaato → pattern fold ke across jodta hai — aksar beech mein hole (diamond / bow).
Open-edge se kaato → original paper ke do opposite kinaron pe same kaat, beech khali nahi.

4. Kaun sa kone?

Do-fold ke baad packet ke 4 kone alag matlab ke hote hain.

Packet ka kone	Original pe kahan	Kholo to
Dono folds ka milna (andar wala)	Paper ka centre	Beech mein 1 hole / 1 kaat
Bilkul open kone	Paper ka bahar wala corner	4 corners pe (agar 2 folds)
Sirf ek fold wali side	Ek midline	Us line pe 2 copies

5. Sawal — basic se pro

Shapes-mirror wala “right→left fold, upar-right punch” aur “4 corners wala 4-parat” yahan nahi.

Q1 · Basic

Square, neeche ki half upar fold. Folded packet ke left-beech mein 1 ched, fold-line pe nahi. Kholo to kitne ched?

Solution

Step 1
1 fold = 2 parat. Punch crease pe nahi → 2 ched.
Step 2
Horizontal fold: copy upar-neeche, left wahi. (Vertical fold hota to left-right copy.)

AnswerB · 2

Q2 · Basic

Wahi horizontal fold. Ched fold-line pe (paper ke horizontal beech). Kholo to kitne?

Solution

Step 1
Punch crease pe = us fold se copy nahi banti. 1 ched, centre line par.

AnswerA · 1

Q3 · Medium

Upar ki half neeche fold (packet = neeche wala rectangle). Punch packet ke neeche-left kone ke paas, fold pe nahi. Kholne par ched kahan?

Folded fold upar (midline), punch neeche-left

Sirf neeche-left
Neeche-left aur upar-left
Neeche-left aur neeche-right
4 corners

Solution

Step 1
Horizontal mirror. Left same. Neeche → upar. Do ched: neeche-left + upar-left.
Step 2
Right tabhi jata jab vertical fold hota. 4 corners ke liye do folds + open-corner punch chahiye.

AnswerB · neeche-left aur upar-left

Q4 · Basic

1 horizontal fold. Do alag ched, dono fold pe nahi. Kholo to kitne ched?

Solution

Step 1
Har punch × 2 parat. 2 × 2 = 4. (Agar ek punch fold pe hota to 2+1=3 — yahan dono fold se door.)

AnswerC · 4

Q5 · Medium

Square, fold along diagonal (triangle packet). Punch triangle ke right-angle kone ke paas (wo original ka ek corner hai), diagonal pe nahi. Kholo?

Folded punch square-kone pe, dash = diagonal

1 ched usi kone pe
2 ched, do opposite corners pe
4 ched
2 ched diagonal ke beech

Solution

Step 1
1 fold = 2 parat. Diagonal B ko D pe map karti hai (opposite corners).
Step 2
Punch corner pe, crease pe nahi → 2 ched, dono square ke opposite corners.

AnswerB · 2, opposite corners

Q6 · Medium

Pehle neeche→upar fold, phir us packet ka left→right fold (4 parat). Punch packet ke beech mein, kisi fold pe nahi (open-corner nahi, centre-crossing nahi). Kholo to kitne ched, kahan?

4 ched, paper ke 4 corners
4 ched, har quadrant ke beech
1 ched paper ke centre
8 ched

Solution

Step 1
2 folds, punch kisi crease pe nahi → 4 ched.
Step 2
Punch quadrant ke centre mein tha, isliye har chhote square ke beech ek ched. Corners nahi (wo open-kone punch hota). Paper-centre nahi (wo dono fold ka crossing hota).

AnswerB · 4, har quadrant ke beech

Q7 · Medium

Horizontal fold (neeche upar). Fold-edge ke beech se ek chhota triangle andar ko kaato (crease se). Kholo to kaun si shape?

Cut on fold-edge maroon = kaat, base crease pe

Upar-neeche kinare pe do nicks
Beech mein diamond / rhombus hole (fold ke across)
4 corners pe triangle
Kuch nahi — fold pe kaat gayab

Solution

Step 1
Base crease pe hai. Unfold: do triangles fold ke do taraf milke diamond. Centre, midline par.
Step 2
Kinaron pe nick tab hota jab open-edge se kaate.

AnswerB · beech diamond

Q8 · Medium

Wahi horizontal fold. Ab triangle open top-edge ke beech se kaato (crease se door). Unfold?

Beech diamond
Upar edge aur neeche edge pe same nick
Sirf upar edge pe nick
Left-right edges pe nick

Solution

Step 1
Packet ka top = original top aligned with original bottom. Dono kinare kat-te hain.
Step 2
Andar hole nahi. Left-right nahi — unpe fold nahi tha.

AnswerB · upar + neeche nick

Q9 · Pro

Q7 wale kaat ke baad khula paper kaun sa?

A diamond beech

B do edge nicks

C 4 gol ched

D diamond vertical fold pe

Solution

Step 1
Fold horizontal tha, kaat crease se. Diamond midline par = A.
Step 2
B = open-edge kaat (Q8). C = punch. D galat fold direction.

AnswerA · diamond beech

Q10 · Pro

Teen baar half-fold (8 parat). Ek ched, kisi crease pe nahi. Kholo to kitne ched?

Solution

Step 1
n=3, k=0 → 2³ = 8.
Step 2
4 tab jab punch ek fold pe ho. 9 koi half-fold rule nahi.

AnswerC · 8

Practice

Pehle khud, phir neeche kholo.

1 2 3 4 5 6 7 8 9 10

Left half ko right pe fold (vertical). Punch packet ke neeche-beech, fold pe nahi. Kholo to ched kahan?

Sirf neeche-right
Neeche-left aur neeche-right, same height
Upar-left aur upar-right
4 corners

Solution

Step 1
Vertical fold → left-right copy, height same. Neeche tha to neeche hi do ched.

AnswerB

1 fold, punch exactly fold pe. Kitne ched?

Solution

Step 1
k=1, n=1 → 2⁰ = 1.

AnswerA · 1

1 fold, teen ched, koi fold pe nahi. Kholo?

Solution

Step 1
3 × 2 = 6.

AnswerC · 6

Diagonal fold. Punch diagonal ke paas lekin us pe nahi. Kitne ched?

1
2
4
Cannot say

Solution

Step 1
Fold pe nahi = 2, dono diagonal ke near, mirror.

AnswerB · 2

2 half-folds (4 parat). Punch dono folds ke crossing pe (original centre). Kitne ched?

Solution

Step 1
n=2, k=2 → 2⁰ = 1. Beech mein ek.

AnswerA · 1

Horizontal fold. Fold-edge se chhota square nick andar. Unfold?

Beech midline par rectangle/hex-jaisa hole (do squares milke)
4 corners pe square
Sirf ek square upar
Kuch nahi

Solution

Step 1
Fold-edge cut → across crease jod. Do square nicks milke beech wala hole.

AnswerA

3 half-folds. Punch ek crease pe (doosri pe nahi). Kitne ched?

Solution

Step 1
n=3, k=1 → 2² = 4.

AnswerB · 4

Vertical fold, punch packet ke left-beech, fold pe nahi. Khula paper kaun sa?

Solution

Step 1
Vertical mirror, same height. Left punch → right copy. A.
Step 2
B = horizontal fold wala pattern. C = fold pe punch. D = khola hi nahi.

AnswerA

2 folds. Cut packet ke andar wale kone se (original centre) chhota triangle. Unfold par kaat kahan?

4 corners
Paper ke beech (centre ke around)
Sirf ek corner
Kinaron pe 2 nicks

Solution

Step 1
Andar wala kone = centre. Unfold: pattern beech mein (chhota rhombus/star-jaisa, folds ke hisaab se).

AnswerB · beech

P10

Sirf ek horizontal fold + punches (fold pe nahi). Kaun sa khula pattern impossible?

Do ched, ek upar-left ek neeche-left (same column)
Do ched, dono upar half mein, koi neeche mirror nahi
Char ched, 2 punches ke 2-2 copies, horizontal symmetry
Ek pair left, ek pair right — har pair upar-neeche mirror

Solution

Step 1
Horizontal fold har punch ko upar-neeche copy karega. Jo pair sirf upar ho, neeche copy na ho — impossible. B.

AnswerB