2. Numbers equal to the fourth power of
their digits: 1634, 8208, 9474.
3. Numbers equal to the fifth power
of their digits: 4150, 4151, 54748, 92727,
93084, 194979.
4. Numbers equal to the sum of the fac-
torials of their digits: 145, 40585. Many
people noted that 2! = 2. Some people treat-
ed 0! as 0, and so missed this solution—but
I’ve always thought of the factorial as the
permutation function, myself, and there’s
only one way to arrange no objects.
5. Number equal to the sum of the sixth
power of its digits: 548834. To verify
uniqueness you don’t have to check that
far. It is easy to see that any eight-digit
number will exceed the sum of the sixth
powers because 8*( 9^ 6) is only seven
digits, and the largest possible seven-
digit number would be 7*( 9^ 6 ), which
is a little over three million.
Solvers
Alexander Alimi, Steve Altschuld,
Keith Anderson, Mark Billingsley,
Andy Blough, Jason Boice, Bob Byrne,
Samantha Casanova, Andrew Dean,
Matthew Deveney, Deb Edwards, David
Ellsworth, Bernie Erickson, Mark Evans,
Drew Forgrave, Renaud Guilbert, Rui
Guo, Kyle Hall, Jason Helbraun, Robert
Himmelstein, Steve Johnson, Kevin
Jones, Ben Kester, Frank Knorr, Eric
Kovach, Douglas Kraft, Nathan Kukla,
Feriz Kurtaljevic, Sam LaDuca, Louis
Lana, James Landon, Yann Lussier,
Bernie Maron, Steve Mathys, Bob
Maguire, Todd Meier, Zach Meier, Lee
Michelson, Brian Miller, Geoff Moak,
Ryan Morgan, Philip Morse, Paul
Navratil, Kyle Nodurft, Don Onnen,
David Promislow, Zach Richards, Bob
Rietz, Daniel Rhodes, Anthony Rubiano,
Beth Sanders, Gregory Savord, Edmund
Scheuermann, Ernesto Schirmacher,
Craig Schmid, Bill Scott, Robert Share,
John Snyder, Don Sondergeld, Eric
Sondergeld, Al Spooner, Steve Streff,
Doug Szper, Donn Takebayashi, David
Treble, Michael Vech, Paul Wright, and
an apology to Stephen Meskin, who
solved the January puzzle but whose
name inadvertently was left off the list.
Actuarial Careers Inc .® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
914-285-5100 | actuarialcareers.com
Actuarial foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
847-706-3535 | actuarialfoundation.org
Actuarial Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
913-451-0044 | arcval.com
AmericanAcademyofActuaries ..................................... 56
202-223-8196 | actuary.org
Andover Research Ltd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
212-986-8484 | andoverresearch.com
Barrie+hibbert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 41
212-553-3913 | www.barrihibb.com
CasualtyActuarialSociety .......................................... 57
703-276-3100 | www.casact.org
Conning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
888-266-6464 | conning.com
DW Simpson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C2
800-837-8338 | dwsimpson.com
Ezra Penland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
800-580-3972 | ezrapenland.com
ggY Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
877-GGy-AXIS | ggyaxis.com
guy Carpenter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
917-937-3251 | www.metarisk.info
Milliman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3, 24-25
206-624-7940 | milliman.com
Pauline Reimer/Pryor Associates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C3
516-935-0100 | ppryor.com
PolySystems Inc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C4
312-332-5670 | polysystems.com
TAI Life Reinsurance Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
708-403-7775 | taire.com
Towers Watson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 15
212-725-7550 | towerswatson.com
Ultimate Risk Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
akutsina@ultirisk.com | ultirisk.com
Valani Consulting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
416-457-8622 | valaniconsulting.com
Winklevoss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
203-861-5530 | winklevoss.com/wintech
WySTAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
800-505-9076 | wystar.com
Ad;Index
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For links to these advertisers’ email addresses and websites,
visit the Contingencies website at contingencies.org/linksto_advert.asp.
