Akuna Capital's 2027 VidCruiter Video Interview can turn a simple picture into a reasoning test. This question rewards candidates who define the random point correctly, translate the boundary condition into geometry, and explain the result without unnecessary algebra.
The real question
Here is the prompt shown in the assessment:
A coin with 3/4 inch diameter is tossed onto a grid with lines separated by 1 inch in both the horizontal and vertical direction. Assume the grid is infinitely large and the lines are infinitely thin. What is the probability the coin lands entirely inside a square on the grid?
How you lose points
- Using the coin's area. The probability depends on where the center may land, not on the circular area divided by the square area.
- Ignoring two dimensions. The center must clear both a vertical line and a horizontal line.
- Using the diameter as the margin. Each boundary needs a clearance equal to the radius, which is 3/8 inch.
- Counting perimeter instead of area. The landing point is uniform over a two-dimensional square.
- Giving only a number. A video response needs a short chain from the allowed center region to the area ratio.
How you pass
A strong answer treats the coin's center as the random point. Inside one 1-inch grid square, the center must stay at least 3/8 inch from every side. That leaves a central square with side length 1 - 2(3/8) = 1/4 inch.
The valid area is therefore (1/4)2 = 1/16 of the unit square. The probability is 1/16. The key insight is that boundary clearance shrinks each linear dimension before the remaining lengths are multiplied.
Get the ones for your role
This is one Akuna Capital assessment question, and its real difficulty is choosing the right geometric object. OpenInterview provides the complete question resources for Akuna Capital so you can practise the full range of reasoning demands.
