I am currently residing in Berkeley, California as the “science communicator in residence” at the Simons Institute. This institute is globally recognized as a hub for collaborative research in theoretical computer science.

One nano-collaboration is today’s puzzle – told to me by a computer scientist at Microsoft I befriended over tea. It’s about data centres – those warehouses containing endless rows of computers that store all our data.

Data centers often encounter the issue of physical machines being unreliable. This is due to the frequent failure of hard drives, which can result in the loss of important data. Companies such as Microsoft have developed methods to retrieve data from failed hard drives. The solution to the following problem is essentially the answer to how they accomplish this.

One potential method for a data center to safeguard its machines against unexpected malfunctions is to have a duplicate machine for each one. This means that if a hard drive were to fail, the information could be retrieved from the duplicate. However, this approach is not commonly implemented due to its high level of inefficiency. For instance, if there are 100 machines, an additional 100 duplicates would be required. Fortunately, there are more effective alternatives, which you may be able to deduce.

The disappearing boxes

You possess 100 boxes, each containing a unique number with no duplicates among them.

You have been informed that one of the randomly selected boxes will be taken away. However, before it is removed, you are given an additional box and permitted to place a single number inside. What number should you put in the extra box to ensure that you can retrieve the number from the removed box?

You are informed that two boxes will be chosen randomly for removal. However, before this happens, you are given two additional boxes and can place one number in each of them. What distinct numbers should you choose to ensure you can retrieve the numbers of both removed boxes?

I will return with the answers at 5pm UK time. In the meantime, please refrain from revealing any information and instead, share your opinions on your preferred hard drives.

The comparison being made is that each box represents a hard drive, the number in the box represents the data, and removing a box symbolizes a hard drive failure. By having an extra hard drive, we are protected from a single random failure, and with two extra drives, we are protected from two failures. It is impressive that we can safeguard a large amount of information from random failures with minimal backup.

The study of “error-correcting codes” encompasses a vast array of elegant principles that offer solutions to problems such as reducing the number of machines required to prevent unexpected malfunctions of hard drives. And these principles have proven effective! Data centers are able to avoid losing data due to mechanical breakdowns.

I had tea with Sivakanth Gopi, a Principal Researcher at Microsoft. He explained that error correcting codes enable us to create dependable systems using imperfect and defective parts. These codes allow us to communicate with individuals even at the farthest reaches of our solar system and securely store massive amounts of data in the cloud. They allow us to ignore the chaos and intricacies of our world and appreciate its splendor instead.

Since 2015, I have been posting a puzzle every other Monday. I am constantly searching for interesting puzzles. If you have one in mind, please email me with your suggestion.

Source: theguardian.com