An isomorphism is a one-to- one and onto map from one space to another which preserves the structure of the space.

1. Mr.’s Downs, Heath , Field, Forest, and Marsh --five elderly pigeon fanciers -- were worried by the depredations of marauding cats owned by five not less elderly spinsters and, hoping to gain control of the cats they married these ladies. The scheme worked well foreach as far as his own cat and pigeons were concerned but it was not long before each cat had claimed a victim and each fancier had lost his favorite pigeon. The Down’s cat killed the pigeon owned by the man who married the owner of the cat that killed Mr. Marsh’s pigeon. Mr. Down’s pigeon was killed by Mrs. Heath’s cat. Mr. Forest’s pigeon was killed by the cat owned by the ladies who married the man whose pigeon was killed by Mrs. Field’s cat. Who was the owner of the pigeon killed by Mrs. Forest’s cat?

2. The Abels, the Beals, the Creens, the Dorians and the Everslys, five families from the midwest, each consisting of a couple with two children, one boy and one girl, got marooned on a deserted island in the Pacific where they lived until long after the children grew up. Nevertheless, even in the limited island society all ten children led long, productive lives fell in love, got married and never divorced. All ten were married before the youngest turned thirty. None married into their parents generation. No marriages involved incest or bigamy and all were heterosexual. The Abel girl married the Beal boy. The Beal girl's husband's sister married the Dorian boy. The Eversley boy's wife's brother married the Creen girl. Who did the Eversley girl marry?

3. An isomorphism is a one-to- one and onto map from one space to another which preserves the structure of the space. Two spaces or situations are isomorphic if there exists an isomorphism from one to the other.

4. Mr.’s Downs, Heath , Field, Forest, and Marsh -- five elderly pigeon fanciers -- were worried by the depredations of marauding cats owned by five not less elderly spinsters and, hoping to gain control of the cats they married these ladies. The scheme worked well for each as far as his own cat and pigeons were concerned but it was not long before each cat had claimed a victim and each fancier had lost his favorite pigeon. The Down’s cat killed the pigeon owned by the man who married the owner of the cat thatkilled Mr. Marsh’s pigeon. Mr. Down’s pigeon was killed by Mrs. Heath’s cat. Mr. Forest’s pigeon was killed bythe cat owned by the ladies who married the man whose pigeon was killed by Mrs. Field’s cat. Who was the owner of the pigeon killed byMrs. Forest’s cat? The Abels, the Beals, the Creens, the Dorians and the Everslys five families from the midwest, each consisting of a couple with two children, one boy and one girl, got marooned on a deserted island in the Pacific where they lived until long after the children grew up. Nevertheless, even in the limited island society all ten children led long, productive lives fell in love, got married and never divorced. All ten were married before the youngest turned thirty. None married into their parents generation. No marriages involved incest or bigamy and all were heterosexual. The Abel girlmarried the Beal boy. The Beal girl's husband's sistermarried the Dorian boy. The Eversley boy's wife's brothermarried the Creen girl. Who did the Eversley girl marry?