The Problem of Zendia

The Call Signs

The call signs consist of three letters, the last of which is a check character according to this construction rule. The alphabet used in this rule consists of 25 letters, the missing letter is Q.

The call signs of each station used on consecutive days form a series. Some examples are:

1st corps:	POH	WCB	YWP	GEP
33rd division:	YWP	GEP	HCO	ZNM
22x. regiment:	HCO	ZNM	ALL	HVV

As easily can be seen, longer strings of call signs can be built. After having converted the first two letters of each call sign in a number (according to: A=0,...,Z=24, AA=0, AB=1,...,BA=25,...,ZZ=624) and computing the difference of consecutive numbers, these differences are (nearly) multiples of 23. Consecutive multiples are:

1	8	3	6	5	4	7	2	9	10	9	2	7	4	5	6	3	8	1	19

The complete string of the 100 call signs actually used is:

Column I = Call sign (in letters)
Column II = Call sign (numerical value)
Column III = Difference to successor
Column IV = (near) multiple of 23
I	II	III	IV	I	II	III	IV	I	II	III	IV	I	II	III	IV	I	II	III	IV
MLH	311	45	2	WPX	540	46	2	FTV	143	47	2	OZU	374	45	2	ZCA	602	46	2
OGN	356	160	7	YLV	586	159	7	HPK	190	160	7	RUA	419	161	7	AYP	23	160	7
VRG	516	92	4	EVW	120	93	4	OAL	350	92	4	YFT	580	91	4	HIR	183	92	4
ZIC	608	115	5	INJ	213	114	5	SSZ	442	114	5	BWO	46	114	5	LAM	275	114	5
DYO	98	137	6	NCM	327	138	6	XGC	556	138	6	GKS	160	138	6	POH	389	138	6
JKR	235	69	3	TPY	465	68	3	CUN	69	68	3	LYD	298	68	3	WCB	527	69	3
MEN	304	183	8	WID	533	184	8	FMT	137	184	8	ORI	366	184	8	YWP	596	183	8
UMF	487	23	1	DSM	92	22	1	MWC	321	23	1	XAA	550	23	1	GEP	154	23	1
VKE	510	437	19	EOU	114	437	19	NUB	344	436	19	XYR	573	436	19	HCO	177	436	19
MXU	322	23	1	XBS	551	23	1	GFH	155	23	1	PJX	384	23	1	ZNM	613	23	1
NVT	345	183	8	XZI	574	183	8	HDG	178	183	8	RHW	407	184	8	ALL	11	184	8
WDT	528	69	3	FHI	132	69	3	OLY	361	69	3	YRF	591	68	3	HVV	195	69	3
YXH	597	137	6	IBF	201	138	6	SFV	430	138	6	BJK	34	138	6	KOS	264	137	6
EJJ	109	115	5	NOR	339	114	5	XTG	568	114	5	GXW	172	114	5	RBU	401	114	5
IZW	224	92	4	TDU	453	93	4	CHJ	57	92	4	LLZ	286	92	4	VPO	515	92	4
MRS	316	160	7	WWZ	546	159	7	FZX	149	161	7	PDV	378	160	7	ZHK	607	160	7
UBT	476	46	2	DFI	80	46	2	MKP	310	45	2	WNN	538	47	2	FSD	142	47	2
VXI	522	206	9	FBG	126	207	9	OFW	355	207	9	YKD	585	206	9	HOT	189	206	9
EDH	103	231	10	NIO	333	230	10	XME	562	230	10	GRU	166	230	10	PVJ	395	(230)	(10)
NJG	334	206	9	XNW	563	205	9	GSL	167	207	9	PWB	396	206	9	EEZ (AAZ)	(0)

The sum of every 20 consecutive differences,

beginning with MXU => 23 (multiple 1), up to EOU => 437 (multiple 19)
beginning with XBS => 23 (multiple 1), up to NUB => 437 (multiple 19)
beginning with GFH => 23 (multiple 1), up to XYR => 437 (multiple 19)
beginning with PJX => 23 (multiple 1), up to HCO => 437 (multiple 19)

is 2729.