Check this website to practice for the INSA test. There are some rumors that INSA takes questions from this site.
Mensa IQ Test
Leetcode with dani
I'll share any new info as soon as I get it!
Mensa IQ Test
Leetcode with dani
I'll share any new info as soon as I get it!
👍4☃1
can u solve this question? the logic is simple but it may take while to figure it out
70. Climbing Stairs
Solved
Easy
You are climbing a staircase. It takes n steps to reach the top.
Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
Example 1:
Input: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
Example 2:
Input: n = 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step
Constraints:
1 <= n <= 45
see the question in leetcode
70. Climbing Stairs
Solved
Easy
You are climbing a staircase. It takes n steps to reach the top.
Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
Example 1:
Input: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
Example 2:
Input: n = 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step
Constraints:
1 <= n <= 45
see the question in leetcode
Leetcode with dani
can u solve this question? the logic is simple but it may take while to figure it out 70. Climbing Stairs Solved Easy You are climbing a staircase. It takes n steps to reach the top. Each time you can either climb 1 or 2 steps. In how many distinct ways…
What if the question asks to use 1,2 and 3 steps?
Leetcode with dani
can u solve this question? the logic is simple but it may take while to figure it out 70. Climbing Stairs Solved Easy You are climbing a staircase. It takes n steps to reach the top. Each time you can either climb 1 or 2 steps. In how many distinct ways…
a, b= 1, 2
for i in range(3,n+1):
a, b = b, a + b
return b
👍5🤯1
Leetcode with dani
What if the question asks to use 1,2 and 3 steps?
a, b, c = 1, 2, 4
for i in range(4, n+1):
a, b, c = b, c, a + b + c
return c
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🔗 Check it out: https://verify.yonathan.tech
Would love your feedback!
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Anonymous Poll
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here is the first question of A2SV weekly contest For G6 i will post each question with their answer
▎🖊 A. Pens and Pencils
▎Problem Statement
Tomorrow is a difficult day for Polycarp: he has to attend lectures and practical classes at the university! He writes lectures with pens and practicals with pencils.
• One pen lasts for
• One pencil lasts for
• His pencil case can hold at most
Can Polycarp pack enough pens and pencils to cover the day?
---
▎Input Format
• First line: An integer
• Each test case: Five integers
–
–
–
–
–
---
▎Output Format
For each test case, output:
• Two integers
–
–
• Or output
---
▎Example Input
▎Example Output
---
▎Explanation
• Test Case 1:
– Needs
– Total =
• Test Case 2:
– Needs
– Total =
• Test Case 3:
– Needs
– Total =
---
▎Sample Code (Python)
▎🖊 A. Pens and Pencils
▎Problem Statement
Tomorrow is a difficult day for Polycarp: he has to attend lectures and practical classes at the university! He writes lectures with pens and practicals with pencils.
• One pen lasts for
c lectures.• One pencil lasts for
d practicals.• His pencil case can hold at most
k writing tools in total.Can Polycarp pack enough pens and pencils to cover the day?
---
▎Input Format
• First line: An integer
t (1 ≤ t ≤ 100), the number of test cases.• Each test case: Five integers
a, b, c, d, k–
a: Number of lectures–
b: Number of practical classes–
c: Lectures per pen–
d: Practicals per pencil–
k: Maximum tools in the pencil case---
▎Output Format
For each test case, output:
• Two integers
x y, where:–
x: Number of pens–
y: Number of pencils• Or output
-1 if it’s not possible to pack enough tools.---
▎Example Input
3
7 5 4 5 8
7 5 4 5 2
20 53 45 26 4
▎Example Output
2 1
-1
1 3
---
▎Explanation
• Test Case 1:
– Needs
ceil(7/4) = 2 pens and ceil(5/5) = 1 pencil.– Total =
2 + 1 = 3 ≤ 8 (possible).• Test Case 2:
– Needs
2 pens and 1 pencil.– Total =
2 + 1 = 3 > 2 (not possible).• Test Case 3:
– Needs
1 pen (ceil(20/45)) and 3 pencils (ceil(53/26)).– Total =
1 + 3 = 4 = 4 (possible).---
▎Sample Code (Python)
t = int(input())
for _ in range(t):
a, b, c, d, k = map(int, input().split())
pens_needed = (a + c - 1) // c # Ceiling of a/c
pencils_needed = (b + d - 1) // d # Ceiling of b/d
if pens_needed + pencils_needed <= k:
print(pens_needed, pencils_needed)
else:
print(-1)
❤3
▎B. Integer Points
▎Problem (brief)
DLS draws
▎Key Fact
The intersection of y = x + p and y = -x + q is given by:
For both x and y to be integers, q and p must have the same parity.
▎Solution
1. Count the number of even and odd integers in sets P and Q.
2. The total number of intersecting pairs is calculated as:
▎Implementation
▎Example
▎Input
▎Output
▎Problem (brief)
DLS draws
n lines of the form y = x + pᵢ and JLS draws m lines of the form y = -x + qⱼ . Count how many pairs (one from each set) intersect at integer coordinates (x, y).▎Key Fact
The intersection of y = x + p and y = -x + q is given by:
x = q - p / 2, y = q + p / 2
For both x and y to be integers, q and p must have the same parity.
▎Solution
1. Count the number of even and odd integers in sets P and Q.
2. The total number of intersecting pairs is calculated as:
Answer = (even_P × even_Q) + (odd_P × odd_Q)
▎Implementation
for _ in range(int(input())):
n, P = int(input()), list(map(int, input().split()))
m, Q = int(input()), list(map(int, input().split()))
eP = sum(p % 2 == 0 for p in P) # Count evens in P
oP = n - eP # Count odds in P
eQ = sum(q % 2 == 0 for q in Q) # Count evens in Q
oQ = m - eQ # Count odds in Q
print(eP * eQ + oP * oQ)
▎Example
▎Input
3
3
1 3 2
2
0 3
1
1
1
1
1
2
1
1
▎Output
3
1
0
❤6
▎C. Labs (Simplified)
You have n² labs numbered from 1 (lowest) to n² (highest).
Any lab u can send 1 unit of water to any lower lab v if u > v .
▎Problem Statement
Split the labs into n groups of size n .
For each ordered pair of groups (A, B) , let f(A, B) be the total units sendable from all labs in A to all in B .
Objective: Maximize the minimum f(A, B) over all A ≠ B .
▎Output
Print any grouping that achieves this.
▎Example
Input:
Output (one possible grouping):
Here, n = 3 , meaning there are labs numbered from 1 to 9.
Every group has 3 labs.
The smallest f(A, B) among all 6 ordered pairs is 4, which is optimal.
Solution
You have n² labs numbered from 1 (lowest) to n² (highest).
Any lab u can send 1 unit of water to any lower lab v if u > v .
▎Problem Statement
Split the labs into n groups of size n .
For each ordered pair of groups (A, B) , let f(A, B) be the total units sendable from all labs in A to all in B .
Objective: Maximize the minimum f(A, B) over all A ≠ B .
▎Output
Print any grouping that achieves this.
▎Example
Input:
3
Output (one possible grouping):
2 8 5
9 3 4
7 6 1
Here, n = 3 , meaning there are labs numbered from 1 to 9.
Every group has 3 labs.
The smallest f(A, B) among all 6 ordered pairs is 4, which is optimal.
Solution
def main():
n = int(input())
groups = [[] for _ in range(n)]
num = 1
for row in range(n):
# decide direction: left‑to‑right on even rows, right‑to‑left on odd
cols = range(n) if row % 2 == 0 else range(n - 1, -1, -1)
for col in cols:
groups[col].append(num)
num += 1
# output
for g in groups:
print(*g)
if __name__ == "__main__":
main()
❤5
▎🧩 D. Add on a Tree (Simplified)
You are given a tree (a connected graph with no cycles) of n nodes. Each edge in the tree initially has a value of 0.
You can perform the following operation:
> Choose any two leaf nodes (nodes connected to only one other node), and a real number x.
> Then, add
🔁 You can repeat this operation as many times as you want, with different pairs of leaves and values.
---
▎❓ Question
Is it possible to reach any possible configuration of real numbers on the edges using a finite number of such operations?
Print:
• YES — if it’s always possible for this tree
• NO — if there exists any configuration that you cannot reach
---
▎📥 Input
• First line:
• Next
It is guaranteed that the graph is a tree.
---
▎📤 Output
• Print YES or NO
---
▎📌 Examples
Input
Output
You are given a tree (a connected graph with no cycles) of n nodes. Each edge in the tree initially has a value of 0.
You can perform the following operation:
> Choose any two leaf nodes (nodes connected to only one other node), and a real number x.
> Then, add
x to all edges on the simple path between these two leaf nodes.🔁 You can repeat this operation as many times as you want, with different pairs of leaves and values.
---
▎❓ Question
Is it possible to reach any possible configuration of real numbers on the edges using a finite number of such operations?
Print:
• YES — if it’s always possible for this tree
• NO — if there exists any configuration that you cannot reach
---
▎📥 Input
• First line:
n — number of nodes (2 ≤ n ≤ 10⁵)• Next
n-1 lines: two integers u and v, meaning an edge between node u and node vIt is guaranteed that the graph is a tree.
---
▎📤 Output
• Print YES or NO
---
▎📌 Examples
Input
2
1 2
Output
YES
Leetcode with dani
▎🧩 D. Add on a Tree (Simplified) You are given a tree (a connected graph with no cycles) of n nodes. Each edge in the tree initially has a value of 0. You can perform the following operation: > Choose any two leaf nodes (nodes connected to only one other…
Answer :
def main():
def iinp(): return (int(input()))
def linp(): return (list(map(int, input().split())))
n = iinp()
arr = [0 for i in range(n+1)]
for i in range(n-1):
u,v = linp()
arr[u] += 1
arr[v] += 1
for i in arr:
if i ==2:
print("NO")
return
print("YES")
main()
E. Nauuo and Cards (Simplified Version)
Nauuo has 2n cards:
n real cards numbered from 1 to n
n empty cards, represented as 0
These cards are randomly shuffled and split into:
Nauuo’s hand → a list of n cards
The pile → another list of n cards, ordered top to bottom
✅ Operation
She can:
Choose any card from her hand, and
Play it — move it to the bottom of the pile,
Then draw the top card of the pile into her hand.
She wants the pile to end up as [1, 2, 3, ..., n] (from top to bottom) as fast as possible.
Nauuo has 2n cards:
n real cards numbered from 1 to n
n empty cards, represented as 0
These cards are randomly shuffled and split into:
Nauuo’s hand → a list of n cards
The pile → another list of n cards, ordered top to bottom
✅ Operation
She can:
Choose any card from her hand, and
Play it — move it to the bottom of the pile,
Then draw the top card of the pile into her hand.
She wants the pile to end up as [1, 2, 3, ..., n] (from top to bottom) as fast as possible.