Brain Teasers Can Require Some Maths

This brain teaser is extracted from my book on how to succeed the first round of interview in consulting firms.


How many numbers between 0 and 1,000 contain the number 5 at least once?
Here we have an example of a brainteaser requiring you to think upfront to avoid wasting a lot of precious time during the interview!
  • You need to be well organized to avoid double and triple counts.
  • Counting the figures by structuring the reasoning by base (1, 10, 100) is possible but takes a long time.
  • A trick is to quantify the following proposal: how many numbers don’t have “5” between 0 and 1,000 at all? If the answer is X, then our result is simply 1,000-X.
  • This process of reasoning is crucial in consulting as a consultant should not put too much effort where the application does not require it.
  • For example, counting all the numbers with 5 will certainly answer the question, but will also provide a partial identification of these numbers, which is off the context of this exercise: it is not requested. Therefore, get straight to the point.
  • The figure of thousands being set to 0, there are 9 possible combinations of the hundreds digit, 9 possible combinations of the tens digit, and 9 possible combinations of the units digit, which is 9 * 9 * 9 = 729 numbers without the number 5 or 1,000 – 729 = 271 numbers with at least a 5 digit.




As you can see this kinds of exercises are not so challenging at the bottom and at the roots. But in a stressful context, most of candidates just fail, so I recommend you train carefully on these exercises to be ready for the D-Day!


Other Resources On Brain Teasers


Links of interest - Introduction To Brain Teasers

- Brain Teasers From Wall Street
Videos on this topic - Classical Brain Teasers
Related concepts- brain teasers finance
- brain teasers questions
- brain teasers consulting
- brain teasers interview