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Three Teasers of the Visual Kind

Problem 1: What is the least number of cubical bricks that can be either spread out to form a square or stacked to form a cube?

Problem 2: Hilary lost one of her cubical building bricks and then found she could make only one solid oblong, whereas previously she could make four different ones. How many bricks were there in the complete set?

Problem 3: John had more building bricks than Hilary. He found he could pack them all together to make a big block in three different ways. How many more bricks did he need to make a solid cube?

Note: Due to confusion over Problem #2, I add this clarification. The resultant oblong shapes involving n blocks are to be 1 block high and yet not 1x1n. Without this clarification, another answer is possible (and perhaps actually better).

 

Source: R. Wesley's (ed.) Mathematics For All, 1956, p. 270


Hint: Get out some colored blocks and start exploring...looking for numerical patterns and relationships.

 


Solution Commentary: In random order, the answers are 36 blocks, 64 blocks, and 4 blocks. Now, how do these answers fit the three questions?