Such lots or parcels of land shall be sold at public vendue to the highest bidder for cash, and shall be offered for sale singly, unless a greater price can be obtained by selling several lots or parcels of land together, in which case several lots or parcels can be sold together after an attempt has been first made to sell the same singly. Such sale may be continued, if necessary, from day to day, for a period not to exceed three (3) days at any one (1) sale. In case all said lands are not sold at the first sale, the sale of the remaining lands shall be advertised as many times as may be necessary to sell said lands, and all sales subsequent to the first sale shall be advertised and conducted the same as the first sale, provided, however, that the judge or corporate authorities may, when petitioned by a majority of the landowners in such town site, withhold from public sale and dedicate to public use such parcels of such town site as are appropriate for public use. No lot or parcel of land shall be sold at less than its appraised value. A new appraisement may be had of all lands remaining unsold: provided, that such new appraisement shall not be made oftener than once every three (3) months. Such new appraisement shall be made by a new board of appraisers, to be appointed in the same manner as the first board of appraisers were appointed, or by the old board of appraisers.