IL-GROSSMAN 1997

Prove that there are at most three primes between $10$ and $10^{10}$ all of whose decimal digits are $1$ .

Is there a planar polygon whose vertices have integer coordinates and whose area is $1/2$ , such that this polygon is (a) a triangle with at least two sides longer than $1000$ ? (b) a triangle whose sides are all longer than $1000$ ? (c) a quadrangle?

Find all real solutions of $\sqrt[4]{13+x}+ \sqrt[4]{14-x} = 3$ .

Prove that if two altitudes of a tetrahedron intersect, then so do the other two altitudes.