PuzzlersWorld.com

How many triangles #5

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1.) How many triangles are there in this triangle ?

how many triangles in this triangle

how many triangles in this triangle

See Answer

Answer: There are a total of 47 triangles

How?
Lets count…
By looking at it, first impression is … its very simple, But mind you! its not that easy !!!
So lets stick to the divide and conquer approach, we will divide this triangle into 3 equal triangles(triangle formed by connecting outer side to the center of the circle) and will count the number of triangles in each part and then by taking two or more parts together.

Number of triangles in one part: 4(non overlapping) + 3(overlapping) = 7 * 3 = 21
Number of triangles by taking two parts together: 8 = 8 * 3 = 24
Number of triangles by taking all three parts together: 2

Thus, total number of triangles in this puzzle are : 21+24+2= 47

How many squares #4

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1.) How many squares do you see in this picture ?

how many squares do you see here

how many squares do you see here

See Answer

Answer with solution

As all the sides are either horizontal or vertical we can say squares diagonals should be parallel. Now to see if the diagonals are parallel or not, i have drawn the diagonals where its not clear if it is a square or rectangle in the image below.

You can see i have labelled few sides as x and y to help you.

So,
Number of squares with side x/2 = 4
Number of squares with side x = 4
Number of squares with side y = 3
Number of squares with side x+y = 6
Number of squares with side x+y = 0
Number of squares with side x+2y = 1
Number of squares with side 2x+2y = 1

Thus, Total number of squares in above puzzle are 19.

How many circles?

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Count the number of circles in the image below.

how many circles do you see in this picture

how many circles do you see in this picture

See Answer

There are a total of 17 circles.

How?
1 black circle in the middle(easily visible to all)
Now move a little away from the screen(16 more circles will be visible easily).
Thus, there are a total of 17 circles.

Find nth element from end of linked list

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How to find nth element from the end of the linked list?

Or in other words Given an integer ‘n’, return a pointer to the n-th node from the end of the list.
Note: Linked list is singly linked list (there is only next pointer no previous pointer).

See Solution: find nth element from end of linked list

Keep two pointers pointer1 and pointer2, both pointing to head of the linked list initially. Increment pointer1 by one node till it reaches (n+1)th node. Now increment both pointers by one node till pointer1 becomes null. At this point the node which pointer2 is pointing to will be the nth node from the last.

Code in C/C++

Node * getNthNodeFromLast(Node * node, int n){
	Node* pointer1 = node;
	Node* pointer2 = node;

	while(pointer1 != null && n > 0){
		pointer1 = pointer1->next;
		n--;
	}
	//List does not have n nodes, so return null
	if(n > 0)
		return null;
	//traverse till pointer1 becomes null
	while(pointer1 != null){
		pointer1 = pointer1->next;
		pointer2 = pointer2->next;
	}
	return pointer2;
}

Find middle element of linked list

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How to Find the middle element of a linked list without traversing twice ?

Linked list is singly linked list(there is only next pointer no previous pointer).

See Solution: Find middle element of a linked list

Take two pointers both pointing to head of the linked list( pointer1 and pointer2 ). Now increment pointer1 by one node and pointer2 by two nodes at a time in a while loop till pointer 2 reaches end of the list or becomes null, at this point the node which pointer1 is pointing to will be the middle element/node of the linked list.

Code in C/C++

Node* getMiddleElement(Node * node){
	Node* pointer1 = node;
	Node* pointer2 = node;

	//traverse till pointer2 reaches end of the list or becomes null
	while(pointer2 != null && pointer2->next != null){
		pointer1 = pointer1->next;
		pointer2 = pointer2->next->next;
	}
	return pointer1;
}

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