How to design a distributed write-heavy data store

It's actually an interview question I'm thinking of for 2 month and can't find a suitable architecture.

The problem

We want to build a small analytics system for fraud detection on orders.

System has the following requirements

• Not allowed to use any technology from the market (MySql, Redis, Hadoop, S3 etc)
• Needs to scale as the data volume grows
• Just a bunch of machines, with disks and decent amount of memory
• 10M Writes/Day

The system needs to provide following API

• /insertOrder(order): Order
  Add an order to the storage. The order can be considered blob with 1-10KBs in size, with an orderId , beginTime, and finishTime as distinguished fields
• /getLongestNOrdersByDuration(n: int, startTime: datetime, endTime: datetime): Order[]
  Retrieve the longest N orders that started between startTime and endTime,
  as measured by duration finishTime - beginTime
• /getShortestNOrdersByDuration(n: int, startTime: datetime, endTime: datetime): Order[]
  Retrieve the shortest N orders that started between startTime and endTime,
  as measured by duration finishTime - beginTime

Look at using druid database. If you time series data

• It should scale well with as volume of data grows
• Time duration queries can be answered effectively

https://druid.apache.org/ - This has been used as analytics db at scale in Fortune 500 companies