The key to this problem is:

• The correct puzzle piece must be PRESENT in all AFFECTED individuals. 
• The correct puzzle piece must be ABSENT from all UNAFFECTED individuals. 

Only one puzzle piece fits these criteria: #36. 

See for yourself:

All affected individuals (1, 3, 6, 8, 10, 11, and 12) must have the deafness puzzle piece. Your first clue is color. Which color puzzle pieces do all affected individuals share? RED. Here's another way to think about it: since Individual #1 on the pedigree is affected and contains only one color, RED, then you know that the puzzle piece representing the mutant gene must be RED as well.

1	2	3
4	5	6
7	8	9
10	11	12

There are lots of red puzzle pieces, though. How do you know which one contains the affected gene? To narrow your choices, find the puzzles of the affected individuals' (1, 3, 6, 8, 10, 11, 12) that have the fewest red pieces. Puzzles 6 and 12 each have 3 red pieces, and puzzle 11 has 4.

Which red pieces do puzzles 6, 11 and 12 share? Only one piece fits the bill: #36.

Now, check your work:

Do all AFFECTED individuals (1, 3, 6, 8, 10, 11, 12) have a red #36 puzzle piece? YES.
Do any UNAFFECTED individuals (2, 4, 5, 7 and 9) have a red #36 puzzle piece? NO. 

Congratulations! You discovered the deafness gene!

Answers to Bonus Questions

Is deafness a recessive or dominant trait? Some types of deafness are recessive and some are dominant traits. Deafness is very likely inherited in a dominant manner if approximately half of all the children born to a parent with deafness also are deaf.

Persons with a recessive deafness trait have two copies of a deafness gene (one inherited from mom and one from dad). If the type of deafness in this example is recessively inherited, the hearing individuals who married into this family and had affected children (a, b, c, d, e, f, g, h, i) were ALL carriers of the deafness gene (pretty unlikely).

Therefore, in this example, deafness is probably a dominant trait. To be certain, though, we'd have to test all individuals in the pedigree to confirm that only affected individuals have the deafness gene.

Is deafness sex-linked? Sex-linked genes are found either on the X or Y chromosome. Genes are rarely found on the Y chromosome, though, so "sex-linked" usually refers to genes on the X chromosome. Remember, females have two X chromosomes (one from mom and one from dad), while males have one X and one Y chromosome (X from mom, Y from dad).

If the deafness gene were sex-linked, then affected fathers would pass the deafness gene to all of their daughters but none of their sons. Affected mothers would pass the deafness gene equally to their sons and daughters. This is not what the pedigree shows. Instead, the pedigree shows that approximately equal numbers of boys and girls are affected by deafness. Therefore, the gene is not sex-linked. 

Since the gene is not sex-linked, it must be found on an "autosome," which is any chromosome other than X or Y.

Bonus Questions A - D

What are the colors of the puzzle pieces that represent the DNA of individuals A, B, C, and D (indicated in the same pedigree below)? What fraction of the total number of puzzle pieces are represented by each color?

Remember, each puzzle represents the total DNA of an individual. Each puzzle piece represents a portion of that DNA.

A The colors of the puzzle pieces are: 1/2 red 1/2 blue.

Since they have the same parents, A and 3 must have the same colors of puzzle pieces. 
3 has 1/2 red and 1/2 blue.
Therefore, A has 1/2 red and 1/2 blue.

B The colors of the puzzle pieces are: all pink.

11's grandparents are B and 8. 
11 inherited 1/4 of her genes from B, 1/4 from 8, and 1/2 from 9 (her mother).
11's puzzle pieces are pink, red, yellow and light blue.
8 and 9 have no pink puzzle pieces, so 11's pink puzzle pieces must have come from B.
Consistent with this, 1/4 of 11's genes are pink.
Therefore, all of B's genes are pink.

C The colors of the puzzle pieces are: all purple.

4's parents are C and D.
4's grandparents (D's parents) are 2 and 3.
Therefore, 4 inherited 1/2 of his genes from C, 1/4 from 2, and 1/4 from 3. 
4 has purple, red, green and blue puzzle pieces.
2 and 3 have no purple puzzle pieces, so 4's purple pieces must have come from C.
1/2 of 4's puzzle pieces are purple.
Therefore, C must have all purple puzzle pieces.

D The colors of the puzzle pieces are: 1/2 green, 1/4 red, 1/4 blue.

D inherited 1/2 his puzzle pieces from 2 and 1/2 from 3. 
2 has only green puzzle pieces, so 1/2 of D's puzzle pieces are green.
3 has 1/2 red and 1/2 blue puzzle pieces, which she passed on to her son D.
Therefore, D has 1/4 red and 1/4 blue puzzle pieces, inherited from 3.

Map a gene activity