Stage: 5 Challenge Level: 
The symbol [ ] means 'the integer part of '.
Consider the three numbers
$$[2x];\ 2[x];\ [x + {1\over 2}] + [x - {1\over 2}]$$
Can they ever be equal?
Can they ever take three different values?
Integers. Inequality/inequalities. Pythagoras' theorem. Quadratic equations. Stage 5 - Reviewed 2012. Mathematical reasoning & proof. Step functions. epsilons. Proof by contradiction. Long problems.
Published November 1998.
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