Can You Solve The Birthday Candles Puzzle? By Professor Henk Tijms’

Thanks to Professor Henk Tijms for this puzzle suggestion! A few years ago I read a probability book by Henk Tijms and really enjoyed it. So I was both surprised and thrilled to get an email from Professor Tijms saying he’s a fan of MindYourDecisions! Today’s problem is adapted from his new book “Probability: A Lively Introduction.” (More precise wording is in the video.) Consider a cake with n candles. What is E(times to blow them all out)? Given: when the cake has k candles, your attempt to blow them out results in a random number of burning candles from 0 to k – 1, each case equally likely.

Professor Henk Tijms

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Books by Henk Tijms I recommend:

Understanding Probability

Probability: A Lively Introduction

Nestor from Barcelona did the problem “the hard way” by solving for the number of ways to blow out k candles in n attempts. I didn’t have a chance to check all the details but it appeared correct on first glance. I thought it would be useful to share; here is the write-up of the solution:

I also apologize the original thumbnail incorrectly stated the problem (saying the max blown out was k – 1 instead of k). I revised the video thumbnail.

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