Arcesium Senior Product Manager Interview Questions and Answers

The king can move only towards the corner and not diagonally. How many ways can a king go from one end of the chessboard to the diagonally opposite square?

• The king can only move towards the corner, so there are limited options for each move

• The total number of moves required to reach the opposite corner is 14

• Using combinatorics, the total number of ways the king can reach the opposite corner is 3432

I want to join GS because of their reputation for excellence and the opportunity to work on challenging projects.

• GS is known for its prestigious reputation in the financial industry

• I am attracted to the opportunity to work on complex and challenging projects

• I admire GS's commitment to innovation and cutting-edge technology

• I believe GS will provide me with valuable learning and growth opportunities

Find max path from bottom left to top right in a matrix using only up and right steps.

• Start from bottom left corner and move towards top right corner.

• At each step, choose the maximum value between the cell above and the cell to the right.

• Keep track of the sum of values in the chosen path.

• The final sum is the maximum possible sum of values in a path from bottom left to top right.

The most likely number to occur as the final sum is 100.

• The sum of the outcomes of the dice rolls will keep increasing until it reaches or exceeds 100.

• Since the dice have equal probabilities for each outcome, the sum will have a higher chance of reaching 100.

• The probability of rolling a sum greater than 100 decreases as the sum gets larger.

Finding probability of point (1,0) lying in longest cut of three random points on circle of radius 1 centered at (0,0)

• The longest cut will be the one that spans the smallest angle between two of the three points

• The probability can be found by calculating the area of the region where the longest cut includes point (1,0)

• This can be done by finding the angle between (1,0) and the two other points and using trigonometry to...read more

Find the magic number in a sorted array where value and index are same.

• Iterate through the array and check if the value and index are same

• If found, return the value

• If not found, return -1

Searching an element in a sorted 2D matrix

• Start from the top-right corner or bottom-left corner

• Compare the target element with the current element

• Move left or down if the target is smaller or move right or up if the target is larger

Design a newspaper subscription system

• Create a user registration system

• Allow users to select subscription plan and payment method

• Provide options for delivery frequency and start/end dates

• Send reminders for subscription renewal

• Allow users to modify or cancel subscription

• Track subscription history and payment records

Number of ways to jump n stairs if a person can climb 1 or 2 stairs.

• Use dynamic programming to solve the problem.

• The number of ways to jump n stairs is equal to the sum of ways to jump n-1 stairs and ways to jump n-2 stairs.

• Base cases: if n=0, return 1 and if n=1, return 1.

An LRU cache can be made using a doubly linked list and a hash map.

• Create a doubly linked list to store the cache items.

• Create a hash map to store the key-value pairs.

• When a new item is added, check if the cache is full. If it is, remove the least recently used item from the linked list and hash map.

• When an item is accessed, move it to the front of the linked list.

• When an item is removed, remove it from both the linked

Probability of winning a dice game where the one with lesser number wins.

• The probability of winning depends on the number of sides on the dice.

• If the dice has an odd number of sides, the probability of winning is higher for the second player.

• If the dice has an even number of sides, the probability of winning is equal for both players.

Compute working days using given functions f, g, and h.

• To compute the 3rd working day, apply function g three times to function f.

• To compute the 2nd working day of the previous month, apply function h to function f, then apply function g twice.

• To compute the 4th working day of the next month, apply function g four times to function f.