NCERT Solutions for Class 4th Maths Chapter 1 Squiggly and Wiggly the spiders; a matchstick puzzle — Let Us Try
Book page 21 Updated on2026-09-19
Q1.
How many triangles are in her web?
Squiggly’s triangular web. Its 12 walls are numbered 1 to 12 and the point A is at the bottom.
Answer
There are 10 triangles in Squiggly’s web.
First the small ones you can see straight away — 6 of them:
the triangle at the very top, above the rectangle;
the triangle at the very bottom, below the rectangle;
inside the rectangle the two slanting walls cross in the middle and make 4 more
triangles — one above, one below, one on the left and one on the right.
Then the bigger ones, each made of two small ones — 4 more:
top-left + left = one big triangle;
top-right + right = one big triangle;
bottom-left + left = one big triangle;
bottom-right + right = one big triangle.
6 small triangles + 4 bigger triangles = 10 triangles
Why it happens: Two small triangles that sit side by side and
share one wall join up into a bigger triangle. So counting only the small ones always
leaves some out.
Q2.
Can she begin at point A and reach back to the same point without walking on any wall more than once? Trace and show Squiggly’s path.
Squiggly’s triangular web. Its 12 walls are numbered 1 to 12 and the point A is at the bottom.
Answer
Yes, she can.
How to be sure: count how many walls meet at each corner of the web.
Corner
Walls meeting there
Even or odd
A (bottom point)
2
even
the top point
2
even
each of the 4 corners of the rectangle
4
even
the crossing point in the middle
4
even
Every corner has an even number of walls, so a walk that
uses each wall once and comes back to the start is possible.
One such path, using the numbers on the walls:
12 → 5 → 4 → 3 → 8 → 7 → 6 → 11 →
10 → 9 → 2 → 1
All 12 walls are used, each exactly once, and she is back at A.
The same web. One walk that uses every wall once is 12, 5, 4, 3, 8, 7, 6, 11, 10, 9, 2, 1.
Why it happens: Every time the spider reaches a corner she
must leave it again, so she uses walls in pairs. That works only if every corner has an
even number of walls — and here every corner does.
Q3.
Her brother, Wiggly made a web using rectangles. How many rectangles can you see in his web?
Wiggly’s web of rectangles, with A at the top and B at the bottom.
Answer
There are 12 rectangles in Wiggly’s web.
Count them in groups, so that none is missed.
Group
How many
the small square room at the top
1
that small room joined to the room below it
1
single rooms in the upper row of the big grid
3
two rooms of the upper row joined side by side
2
all three rooms of the upper row together
1
the two closed rooms in the lower row
2
each of those two rooms joined to the room above it
2
Total
12
Tip: The middle room of the bottom row has no wall along
its bottom, so it is not a rectangle. Watch out for it.
Why it happens: A rectangle needs all four of its walls to be
there. Two or three rooms side by side also make one bigger rectangle, so those must be
counted as well.
Q4.
Can he begin at point A and leave from point B without walking on any wall more than once? Trace and show Wiggly’s path.
Wiggly’s web of rectangles, with A at the top and B at the bottom.
Answer
No, he cannot.
Why not: count the walls at every corner of the web.
At almost every corner an even number of walls meet — 2 or 4.
Only two corners have an odd number: the corner at the
far left of the middle line and the corner at the far right of the middle line. At each
of those, 3 walls meet.
A walk that uses every wall once must start at one odd corner and finish at the
other.
A and B are not those corners — at A only 2 walls meet, and at B only 2 walls
meet. Both are even.
So Wiggly cannot go from A to B using every wall exactly once.
The same web. The two ringed corners are the only corners where an odd number of walls meet.
Try This: If he starts at the left middle corner, he
can walk along every wall once and come out at the right middle corner.
Why it happens: At every corner in the middle of a walk the
spider goes in by one wall and out by another, so those corners need an even number of
walls. Only the starting corner and the finishing corner may be odd.
Q5.
Use 5 matchsticks to make 2 triangles. Then draw it in the space provided.
The five matchsticks shown in the book.
Answer
Make the two triangles share one matchstick.
Lay 1 matchstick standing up in the middle. This is the shared side.
Put 2 matchsticks on its left so that they meet its two ends — that is the first
triangle.
Put the other 2 matchsticks on its right in the same way — that is the second
triangle.
2 + 2 + 1 shared stick = 5 matchsticks, and 2 triangles
Two separate triangles would have needed 3 + 3 = 6 sticks.
The shape you get looks like a diamond with a line down the middle.
Why it happens: Sharing a side saves one stick, because that one
stick does the work of two.