From left to right, the arrangement in which everyone will appear the same height is:
Pup, Bro (striped shirt), Dad (red shirt), Mom (blue top), Sis (orange top).
Imagine that the holes are numbered 1 through 5 from left to right. The family members
are shown as having segments that represent units of height. In the first picture, 8 segments of
Mom are showing; let's assume she is 9 units tall, in which case hole #1 is 1 unit deep. (Only the
relative lengths and depths matter. The solution will be identical if we assume that Mom is 12 units
tall and hole #1 is 4 units deep, etc.) Since Mom projects 8 units above hole #1 and only 4 units
above hole #3 in the second picture, hole #3 must be 1 + 4 = 5 units deep. Sis stands 2 units above
hole #3 and 5 units above hole #5, so hole #5 is 5 -3 = 2 units deep. Dad sticks out 8 units above
hole #5 and 6 units above hole #4, so hole #4 is 2 + 2 = 4 units deep. Pup stands 2 units above hole
#4 and 3 units above hole #2, so hole #2 is 4- 1 = 3 units deep. So from left to right the holes are
1, 3, 5, 4, and 2 units deep.
The heights of the family members are their visible lengths plus the
depths of the holes.
Mom 9 units tall, Bro 8 units, Sis is 7 units, Pup is 6 units,
and Dad is 10 units.
To make everyone appear the same height, Pup (6 units tall) is in the 1-unit hole
#1, Bro (8 units) is in the 3-unit hole #2, Dad (10 units) is in the 5-unit hole #3, Mom (9 units) is
in the 4-unit hole #4, and Sis (7 units) is in the 2-unit hole #5.
Here is another way to solve it:
From the first picture,
Mom = 8 units above ground
Bro = 5
Sis = 2
Pup = 2
Dad = 8
From the second picture,
Mom = 4 units above ground
Bro = 7
Sis = 5
Pup = 3
Dad = 6
Comparing the same people in each hole,
M = B + 1
B = P + 2
S = M - 2
P = D - 4
D = S + 3
Solving simultaneously, you can express everyone in terms of Pup:
P
S = P + 1
B = P + 2
M = P + 3
D = P + 5
Then using some logic, you can determine the depths of the hole and where each must stand.
