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:

33rd division:YWPGEPHCOZNM
22x. regiment:HCOZNMALLHVV

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:


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          
MLH311452   WPX540462   FTV143472   OZU374452   ZCA602462
OGN3561607 YLV5861597 HPK1901607 RUA4191617 AYP231607
VRG516924 EVW120934 OAL350924 YFT580914 HIR183924
ZIC6081155 INJ2131145 SSZ4421145 BWO461145 LAM2751145
DYO981376 NCM3271386 XGC5561386 GKS1601386 POH3891386
JKR235693 TPY465683 CUN69683 LYD298683 WCB527693
MEN3041838 WID5331848 FMT1371848 ORI3661848 YWP5961838
UMF487231 DSM92221 MWC321231 XAA550231 GEP154231
VKE51043719 EOU11443719 NUB34443619 XYR57343619 HCO17743619
MXU322231 XBS551231 GFH155231 PJX384231 ZNM613231
NVT3451838 XZI5741838 HDG1781838 RHW4071848 ALL111848
WDT528693 FHI132693 OLY361693 YRF591683 HVV195693
YXH5971376 IBF2011386 SFV4301386 BJK341386 KOS2641376
EJJ1091155 NOR3391145 XTG5681145 GXW1721145 RBU4011145
IZW224924 TDU453934 CHJ57924 LLZ286924 VPO515924
MRS3161607 WWZ5461597 FZX1491617 PDV3781607 ZHK6071607
UBT476462 DFI80462 MKP310452 WNN538472 FSD142472
VXI5222069 FBG1262079 OFW3552079 YKD5852069 HOT1892069
EDH10323110 NIO33323010 XME56223010 GRU16623010 PVJ395(230)(10)
NJG3342069 XNW5632059 GSL1672079 PWB3962069 EEZ

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.

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© Karlheinz Everts