# A deep thought puzzle

Thursday 9th December 2021

One number is removed from the set of consecutive integers from $$1$$ to $$n$$. The average of the remaining numbers is $$40$$. Which integer was removed? (A hint for students can be found at the end of this article!)

What do you call problems that can be simply explained and yet take a significant amount of reasoning?

You could call them perfect lesson starters to write up while getting things ready for the class. You could equally call them good questions to give in practice interviews, especially for online interviews.

This problem was one of a set that we used in our regional Teacher Network meeting on preparing students for academic interviews. Ideal problems will be ones for which students understand the idea but have to extemporise and cope with getting stuck. Teachers came together to experience interviewing from both sides, in particular choosing good prompts for students who got stuck or set off on an unhelpful track. Teachers who attended shared their expertise and experience, and we'd like to thank them for their active involvement.

A good source of questions can be found in the TBO Problem Solving Booklet on the DrFrostMaths website.

Next term we're planning a Teacher Network meeting with a focus on mastery at A level. We're also setting up a series of one-hour professional development snippets touching upon the following: student use of technology with devices and calculators, developing Core Maths, working with the large data set, and creating a suitably demanding post-16 lesson. If you'd like to receive updates when these events are available to book, you can subscribe to receive our latest news.

Try thinking about possibilities for $$n$$ linked to the value for the mean and the denominator of $$4$$.