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# Little Difference

Without using a calculator, or performing any long multiplication calculations, find the value of:

What about $2016×2018-2017^2?$

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Age 14 to 16

ShortChallenge Level

- Problem
- Solutions

Without using a calculator, or performing any long multiplication calculations, find the value of:

$2015×2017-2016^2$

What about $2016×2018-2017^2?$

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?