We present three simple regular one-dimensional variational problemsthat present the Lavrentiev gap phenomenon, i.e., inf$\{\int_a^b L(t,x,\dot x): x\in W_0^{1,1}(a,b)\} $(where $ W_0^{1,p}(a,b)$ denote the usual Sobolev spaces withzero boundary conditions), in which in the first example the twoinfima are actually minima, in the second example the infimum in$ W_0^{1,\infty}(a,b)$ is attained while the infimum in $W_0^{1,1}(a,b)$ is not, and in the third example both infimum arenot attained. We discuss also how to construct energies with a gapbetween any space and energies with multi-gaps.