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# A Puzzle For College

FreshBooks is hiring co-op students, so a few of us zipped up to Waterloo yesterday to chat with university students about working at FreshBooks. We talked about working on big production systems with tons of users who really rely on your work day in and day out, about having the freedom to figure out your own solutions and use your favourite tools, and how much I love hitting people with Nerf swords.

We also gave the students a puzzle — first person to supply a correct answer would win a gift certificate (and show us that they’re pretty smart, too). Here’s the puzzle:

Suppose we sent a million invoices this month, a quarter of them on the first, a sixteenth on the second, and so forth.

On the first we send a quarter of them (rounded up), then each subsequent day we send a quarter of what remains, until the last day, when all the remaining ones for the month are sent.

Every weekday in a month adds 0.25% to the total for next month, compounded and rounded down (once).

So since there are 21 weekdays in January, next month we’ll be sending:

floor(1,000,000 1.0025 … * 1.0025)

= floor(1053833.517…)

= 1053833

So, Feb 1st would be ceil(1053833/4) = 263459. [corrected]

Pay no attention to holidays, a weekday is just a weekday.

If this keeps up, how many invoices would we send on each of January 31st and February 1st 2020?

We’re still receiving responses, so don’t post an answer in the comments yet! But feel free to brag that you KNOW the answer…

It was great meeting all the folks who came out for our Waterloo event. We enjoyed the whole experience and are looking forward to talking FreshBooks at more colleges around the Toronto area. If you’re at university somewhere around here and are interested in coming aboard the FreshBooks team, please email us at “careers@freshbooks.com” and we’ll chat!

[Apologies for the mistake in the opening paragraph of the written puzzle; I read out the right thing, and wrote it down quite wrongly. —ashok]

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