Despite some differences in appearance and habits, men and mice are genetically very similar. In a pioneering paper, Nadeau and Taylor, 1984 estimated that surprisingly few genomic rearrangements (about 200) have happened since the divergence of human and mouse 75 million years ago. Every genome rearrangement study involves solving a combinatorial puzzle to find a series of genome rearrangements to transform one genome into another. I will briefly describe some genome rearrangements algorithms and show how these algorithms shed light on previously unknown features of mammalian evolution. In particular, they provide evidence for extensive re-use of breakpoints from the same relatively short regions and reveal a great variability in the rate of micro-rearrangements along the genome. Our analysis also implies the existence of a large number of very short ``hidden'' synteny blocks that were invisible in comparative mapping data and were ignored in previous studies of chromosome evolution. These results suggest a new model of chromosome evolution that postulates that breakpoints are chosen from relatively short fragile regions that have much higher propensity for rearrangements than the rest of the genome. This is a joint work with Glenn Tesler.