Basic Alphametics (Solution)
by David Farhi and Casey McNamara
You have to figure out the consistent mapping of letters to numbers that makes each addition valid in a different base. As is usually the case for alphametic puzzles, each letter is mapped to a different number; furthermore, in this puzzle, the mapping is the same for all the alphametics. The solution is:
N=0 O=1 P=2 I=3 T=4 E=5 S=6 U=7 L=8 G=9 C=10 A=11 Z=12 K=13 Y=14 M=15 J=16 R=17 Q=18 F=19 X=20 D=21 H=22 W=23 B=24 V=25
The bases that the puzzles work in, then, are: 6, 25, 11, 8, 24, 11, 17, 21. Using the letters-to-numbers conversion above, that gives: SVALBARD.