If the map requires that the pickaxe (and/or other tools) are thrown away you could use chests at puzzles with limited amount of blocks stored inside, requiring that the player must figure out how to use the blocks to beat the puzzle. Sand can be particularly useful in this case because of how it is affected by gravity. However, since the player would effectively only have one shot at trying to beat the puzzle it would probably be best if this puzzle was not required to be beaten to carry on with the adventure but would give a good reward if the succeeded in doing so.