I already know the dimensions of the
three squares. They’re in my office, after
all, and I do have a tape measure.
The puzzle arises from the fact that
my mom is sending me a box with all my
old D&D figurines, requiring me to get a
bigger display case. In fact, I’m going to
need 7 square feet of space on the bottom and middle squares. So please, find
the dimensions of the three squares, in
arithmatic progression, with a common
difference of 7 square feet.
You might want to try the three
squares with a common difference of 5
square feet as a warm-up.
with a common difference of 7 square
feet have edges of 11. 3 inches, 33. 7 inches, and 46. 3 inches.
If you got the warm-up but not the
puzzle and are now feeling angry that
you didn’t think of going to fractional values, you might try finding three
squares with a common difference of 13
square feet. As a hint, that would be far
too big for my office.
Solvers
Robert Bartholomew, Scott Boulay,
Bob Byrne, Eduardo Caro,
Andrew Dean, Bill Glasgow,
Rui Guo, Adam Hickman, Lee
Michelson, Geoff Moak, Anil Narale,
David Oakden, David Promislow,
Tomasz Serbinowski, Lenny Shteyman,
Al Spooner, Kevin Trapp, Alex
Zaslavskiy
Solution
First let’s consider the warm-up: Obviously, the equation x2 – y2 = y2 – z2 =
5 has infinitely many solutions in real
numbers. So we must restrict ourselves
to make it interesting enough to count as
a puzzle. But if you limit yourself to the
integers, there’s only one solution to the
difference of squares equaling 5, namely
9 – 4. Just because I expressed the difference in square feet, however, doesn’t
mean that feet are the best unit to use.
If you consider that 5 square feet is 720
square inches, you can then proceed by
factoring and some thought—or by trial
and error. Either way you’ll quickly find
that the three squares with a common
difference of 5 square feet have edges of
31 inches, 41 inches, and 49 inches.
Now here’s where I have to confess
to a touch of sadism—after the warm-up,
you reasonably might have thought the
same approach would work for the puzzle itself. That is, 7 square feet is 1,008
square inches, find three square integers,
etc. Well, no—there’s no integer solution
to x2 – y2 = y2 – z2 = 1,008. That is, there
are multiple differences of squares that
come to 1,008, but no two pairs have a
common term. So for this part, you have
to go to fractions. Many people reported
some frustration at not finding a solution in the common fractions associated
with inches—one-quarter, one-eighth,
etc. Sorry about that. The three squares
Ace Tempest Life re ...................... 83
203-328-7000 | www.acetempestlifereusa.com
Actuarial Careers, inc.®..................... 5
914-285-5100 | www.actuarialcareers.com
ActuarialFoundation ..................... 91
847-706-3535 | www.actuarialfoundation.org
Actuarial resources ...................... 13
913-451-0044 | www.arcval.com
American Academy of Actuaries. . . . . . . . . . . . 74
202-223-8196 | www.actuary.org
AndoverresearchLtd...................... 7
212-986-8484 | www.andoverresearch.com
Aon Benfield .......................... 56, C4
215-255-4044 | www.aonbenfield.com
Buck Consultants ........................ 19
866-355-6647 | www.buckconsultants.com
Claim Analytics .......................... 95
416-733-9541 | www.claimanalytics.com
CPS, inc. ................................ 61
708-531-8289 | www.cps4jobs.com
Darwin rhodes ........................... 59
212-918-4754 | www.darwinrhodes.com
DFA Capital Management .................. 29
914-701-7200 | www.dfa.com
D.W. Simpson ............................ C2
800-837-8338 | www.dwsimpson.com
Elliott Bauer ............................. 21
+1-778-373-1519 | www.elliottbauer.com
EMB America LLC ........................ 15
858-793-1425 | www.embamerica.com
Ernst & Young ........................... 47
www.ey.com | michael.hughes@ey.com
generali uSA Life reassurance . . . . . . . . . . . . . 77
877-436-8330 | www.generaliusalifere.com
ggY Axis ............................... 11
877-GGY-AXIS | www.ggyaxis.com
Hannover Life reassurance . . . . . . . . . . . . . . . . 81
800-327-1910 | www.hlramerica.com
insureware ........................... 50–51
+ 61 3 9533 6333 | 386-673-1919
www.insureware.com
Jacobson ............................ 25, 57
800-466-1578 | www.jacobsononline.com
JPMorgan............................... 65
312-732-2111
www.jpmorgan.com/cbs/actuaries
Lewis&Ellis............................. 71
913-491-3388 | www.lewisellis.com
Lynchval................................ 23
703-709-1000 | www.lynchval.com
Mid America Search ...................... 67
800-200-1986 | www.midamericasearch.com
Milliman ........................... 3, 40–41
206-624-7940 | www.milliman.com
Munich American reassurance . . . . . . . . . . . . . 73
770-350-3200 | www.marclife.com
Optimum re insurance .................... 38
214-528-2020 | www.optimumre.com
Pinnaclegroup........................... 27
800-308-7205 | www.pinnaclejobs.com
PolySystems, inc. ........................ C3
312-332-5670 | www.polysystems.com
Pryor Associates/Pauline reimer . . . . . . . . . . . 75
516-935-0100 | www.ppryor.com
rgAreinsurance......................... 49
636-736-7376 | www.rgare.com
S.C.international Ltd....................... 1
800-543-2553 | www.scinternational.com
Stewart Search .......................... 78
888-Job-oPEN | www.stewartsearch.com
Sungard ................................ 79
800-825-2518
Swissre................................ 53
800-376-4647 | www.swissre.com
TAi Life reinsurance Systems . . . . . . . . . . . . . . 14
708-403-7775 | www.taire.com
Towers Perrin. . . . . . . . . . . . . . . . . . . . . . . . . 17, 31
904-391-1900 | www.towersperrin.com/tillinghast
Transamerica reinsurance . . . . . . . . . . . . . . . . . 87
704-344-4208 | www.transamericareinsurance.com
ultimaterisk Solutions ................... 69
akutsina@ultirisk.com | www.ultirisk.com
Valani Consulting ........................ 39
416-417-0181 | www.valaniconsulting.com
Watson Wyatt............................ 9
212-252-8060 | www.watsonwyatt.com
Winklevoss.............................. 85
203-861-5530 | www.winklevoss.com/wintech
Ad Index
To add your company’s name to this list, call Mohanna Sales Representatives at
972-596-8777 or e-mail info@mohanna.com.
For links to these advertisers’ e-mail addresses and websites, visit the Contingencies
website at www.contingencies.org/linksto_advert.asp.
