A compound C${}_4$H${}_{10}$O${}_2$ consumes one mole of $\mathrm{HIO}{}_4$ per mole and gives a single organic product, which gives a silver mirror with Tollens reagent and a yellow precipitate with $\mathrm{I}{}_2/\mathrm{NaOH}$. The compound is

Cleavage by $\mathrm{HIO}{}_4$ requires a vicinal diol, which excludes butane-1,4-diol. Butane-1,2-diol gives $\mathrm{HCHO}$ and propanal, and 2-methylpropane-1,2-diol gives $\mathrm{HCHO}$ and propanone, i.e. two different products. Only symmetrical butane-2,3-diol gives a single product, 2 $\mathrm{CH}{}_3\mathrm{CHO}$, which is Tollens and iodoform positive.