For each and for all , construct a continuous function such that there do not exist with for which
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$(SWE 2)$ For each $\lambda (0 < \lambda < 1$ and $\lambda = \frac{1}{n}$ for all $n = 1, 2, 3, \cdots)$, construct a continuous function $f$ such that there do not exist $x, y$ with $0 < \lambda < y = x + \lambda \le 1$ for which $f(x) = f(y).$
Izvor: Međunarodna matematička olimpijada, shortlist 1969
Školjka 
For each 
and 
for all 
, construct a continuous function 
such that there do not exist 
with 
for which 