Katkat
Back

Solve Coin, Growth, Time, and Rate Problems

Epic SystemsSoftware Engineer · Online Assessment
MediumSoftware EngineerOnline AssessmentStatistics & Math

Last updated

This problem tests analytical thinking and basic arithmetic under time pressure, focusing on rate of change and compound logic.

The Lily Pad Paradox

In a local pond, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire pond, answer the following logic-based math questions.

Task 1: The Timeline

On what day was the pond exactly one-quarter covered?

Task 2: The Parallel Rate

Suppose a second patch of lilies is introduced on Day 1, but this patch triples in size every day. If this second patch starts at the same size as the first patch on Day 1, on which day will the second patch alone cover the entire pond?

Task 3: Coin Logic

You have a collection of 30 coins consisting of nickels ($0.05) and dimes ($0.10). The total value of the coins is $2.25. How many of each coin do you possess?

Constraints & Examples

  • Ensure you account for the exponential nature of growth.
  • For Task 3, define the system of equations clearly before solving.
  • Example: If a patch doubles every day and covers the pond on Day 10, it covered half the pond on Day 9. Use this logic for Task 1.

Edge Cases

  • Consider if the growth rate is applied at the start or end of the day.
  • Ensure your coin counts are non-negative integers.

Hints

Hint 1

For Task 1, work backward: if it is full on Day 48, how full is it on Day 47?

Hint 2

For Task 2, express the growth of the second patch as 3^(n-1) and set it equal to the total capacity.

Hint 3

For Task 3, use the system: n + d = 30 and 0.05n + 0.10d = 2.25.

Follow-up questions

  • What happens to the timeline in Task 1 if the patch quadruples every day instead of doubling?
  • If you add a third type of coin (quarters) to the collection, what additional information would you need to solve for the exact number of each?
  • How would you optimize an algorithm to calculate the size of the patch on Day N for any growth rate r?