CCNY Mathematics/puzzle

LUCAS-BONACCIO FARM, 1998
A C R O S S N U M B E R P U Z Z L E

ACROSS
1 Length of a side of corn field (yards)
4 Twice the age of Nancy
6 Year Grand Pa was born
7 Total sale value of livestock ($ mod 10000)
9 Total age of four children
10 Maternal prime factor of 11-down
12 Total heads of livestock (mod 100)
14 Perimeter of rectangular barn (feet)
16 Length of barn (feet)
17 One side of triangular wheat field (yards)
20 Shortest side of wheat field (yards) whose opposite angle is half another.
21 One side of wheat field (yards)
22 Number of hogs
24 Square of Mary's age
26 Number of lambs
27 Paternal prime factor of 11-down
30 Average sale value of a hog ($)
31 Perimeter of triangular corn field (yards)
33 House number
36 Age of Grand Ma (not as old as Grand Pa)
37* Width of barn (feet)
*The clue in a previous version was incorrect and referred to thewheat field.

DOWN
1 Bob Lucas' age, which is three times John's
2 Grand Pa's age
3 Average yield of potatoes (cwt/acre)
4 Average weight of a hog (pounds)
5 Average weight of a lamb (pounds)
6 Average sale value of a lamb ($)
7 Average yield of corn (bushels/acre)
8 Average weight of a yearling steer (pounds)
11 Lucas-Bonaccio's phone number
13 Cube of John's age
15 Area of barn (square feet)
16 Product of ages of four children
17 Total acreage (acres)
18 Average sale value of a steer ($)
19 Perimeter of wheat field (yards)
23 Length of longest side of corn field (yards), with its opposite angle twice another
25 Length of side of corn field (yards)
27 Non-tillable acreage (acres)
28 Number of yearling steers
29 Square of age of youngest child, Mark
32 Tillable acreage (acres)
34 Coincidental index to 11-down? (or Rosa's age)
35 Number of years Bob and Rosa Bonaccio are married

About the Crossnumber Puzzle

Lucas-Bonaccio Farm, 1998 was inspired by another cross-number puzzle: Dog's Mead and the Dunk Family, and was presented to the Math Club at City College on April 24, 1998.

Bob Lucas and Rosa Bonaccio have been happily married for a number of years. They have four children: two boys, Mark and John, and two girls, Mary and Nancy. They live with Grand Pa and Grand Ma in a large stone front colonial home in Idaho with commanding valley views from a lofty setting. Their farm, though expansive, has only a relatively small area for planting. This tillable area includes two triangular fields on which they plant wheat and corn. They plant potatoes on the remaining fertile soil. The balance of the farm consists of a few hundred acres of pasture and woods. The Lucas family raises livestocks, which include steers, hogs and lambs. The children love to feed the animals, and sometimes they play and help out in the barn.

Both Bob Lucas and Rosa Bonaccio are proud of their family lineages. Rosa claims to be a direct descendent of the famous Leonardo of Pisa, who introduced the Arabic numeral notation to Europe in a book Liber abaci published in 1202. In this book, Leonardo posed a problem on rabbits, the solution of which became known as the Fibonacci sequence. A distant ancestor of Bob, Edouard Lucas, wrote about the problem during the last century, and generalized the sequence to the Lucas sequence (which is similar to the Fibonacci sequence, but begins with 1, 3, 4, 7, ... instead of 1, 1, 2, 3, ...). The telephone number occurs among the Fibonacci sequence, and has a rare property. (E. Lucas, by the way, also invented the Tower of Hanoi problem that every beginning computer science student has to solve.)

You can find out a lot more about the Lucas family by solving the puzzle, which requires a combination of logic, number theory, computing and programming skills, trigonometry, trial and error, and of course, some knowledge about farming.