Rob was looking at his collection of band concert programs, from all the band concerts that he has ever been in. There were less than 100
programs altogether. He started organizing the programs into piles. He
put all the programs into piles of 4, but found there were three left
over. So then he put them in piles of 5, and again found there were 3
left over. Next he tried putting them into piles of 7, and this time found
there were 6 left over. Finally he put them into piles of 3, and this time
there were 2 left over. So he gave up and stuck them back in the drawer
where he found them. How many programs does Rob have?