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.

• 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