Cipher Challenge
The Mathematics of Waiting
Introduction
An explanatory account of queues, arrival patterns, service rates, and why waiting time often feels unpredictable.
Count overlapping units and compare their distributions.
Live output703 overlapping units
| Unit | Count | Share | Rank |
|---|---|---|---|
| S | 93 | 13.2% | 1 |
| C | 74 | 10.5% | 2 |
| Q | 60 | 8.5% | 3 |
| H | 54 | 7.7% | 4 |
| F | 49 | 7.0% | 5 |
| U | 47 | 6.7% | 6 |
| T | 43 | 6.1% | 7 |
| M | 37 | 5.3% | 8 |
| W | 34 | 4.8% | 9 |
| R | 28 | 4.0% | 10 |
| J | 24 | 3.4% | 11 |
| A | 22 | 3.1% | 12 |
1
VCHQHTX QHPS HU SOJSFHSTRSA
25
JSFUWTCMMG ZIQ JMCTTSA
45
UQCQHUQHRCMMG. C ZIU
62
JCUUSTXSF TWQHRSU QES
81
HTQSFBCM UHTRS QES MCUQ
101
CFFHBCM, VEHMS C QFCTUHQ
121
CXSTRG UQIAHSU QEWIUCTAU WY
145
HTQSFBCMU CRFWUU CT STQHFS
168
FWIQS. HY BSEHRMSU CFFHBS
189
ITJFSAHRQCZMG, JSWJMS VEW
211
FSCRE C UQWJ CQ FCTAWP CFS PWFS
236
MHDSMG QW STRWITQSF C MWTX XCJ
261
QECT C UEWFQ WTS. QEHU SYYSRQ
284
ESMJU SOJMCHT VEG CBSFCXS
306
FSJWFQSA VCHQU RCT SORSSA
328
UHPJMS QHPSQCZMS
343
SOJSRQCQHWTU. KISISU
361
HTQFWAIRS WQESF
375
FSMCQHWTUEHJU CPWTX CFFHBCM
400
FCQS, USFBHRS FCQS, CTA
418
BCFHCZHMHQG. C UGUQSP
436
WJSFCQHTX TSCF YIMM RCJCRHQG
461
PCG ASBSMWJ ASMCGU KIHRDMG
484
ZSRCIUS HQ ECU MHQQMS FWWP QW
508
CZUWFZ AHUFIJQHWTU. CAAHTX C
532
UPCMM ZIYYSF RCT HPJFWBS
553
FSMHCZHMHQG PWFS QECT
572
ASPCTAHTX JSFYSRQ UJSSA YFWP
597
SBSFG UQSJ. PCQESPCQHRU AWSU
621
TWQ PCDS VCHQHTX JMSCUCTQ, ZIQ
646
HQ FSBSCMU VEG RSFQCHT ASMCGU
671
FSRIF CTA VEHRE RECTXSU PCG
694
FSAIRS QESP.
Compare word shapes, terminals, contacts, and reversals.
Live output129 words · 109 distinct
| Word | Pattern | Count | Start positions |
|---|---|---|---|
C | 1 | 7 | 58, 113, 216, 253, 265, 429 +1 |
VCHQHTX | 1.2.3.4.3.5.6 | 2 | 1, 628 |
ZIQ | 1.2.3 | 2 | 35, 643 |
QES | 1.2.3 | 2 | 78, 94 |
CFFHBCM | 1.2.2.3.4.1.5 | 2 | 101, 393 |
PWFS | 1.2.3.4 | 2 | 232, 564 |
QW | 1.2 | 2 | 242, 506 |
QECT | 1.2.3.4 | 2 | 261, 568 |
VEG | 1.2.3 | 2 | 296, 655 |
RCT | 1.2.3 | 2 | 319, 543 |
FCQS | 1.2.3.4 | 2 | 400, 411 |
CTA | 1.2.3 | 2 | 415, 676 |
Terminals
| Sequence | Initial | Final |
|---|---|---|
FS | 7 | 4 |
QE | 7 | 0 |
TX | 0 | 7 |
SU | 0 | 6 |
CT | 3 | 5 |
HTX | 0 | 5 |
MG | 0 | 5 |
MS | 0 | 5 |
SA | 0 | 5 |
VE | 5 | 0 |
AS | 4 | 0 |
CF | 4 | 1 |
Contacts
| Letter | Left | Right |
|---|---|---|
A | 6: S 7, T 5, A 1, C 1, I 1, W 1 | 6: H 5, S 4, I 2, W 2, A 1, U 1 |
B | 5: F 3, H 3, S 3, C 1, W 1 | 3: S 7, C 5, H 1 |
C | 14: P 7, F 6, M 6, B 5, Q 5, R 5, E 4, S 4, V 3, H 2, J 2, U 2, T 1, X 1 | 16: T 14, Q 9, M 8, F 6, H 5, Z 5, G 4, U 4, R 3, J 2, X 2, A 1, B 1, D 1, I 1, P 1 |
D | 3: C 1, H 1, R 1 | 2: S 2, M 1 |
E | 5: Q 9, V 5, R 3, U 2, S 1 | 5: S 6, H 5, C 4, W 3, G 2 |
F | 11: S 14, C 6, W 5, F 3, J 2, Q 2, H 1, I 1, R 1, U 1, Y 1 | 12: S 12, C 6, W 6, H 5, B 3, F 3, Q 3, G 1, I 1, U 1, Y 1, Z 1 |
G | 7: M 5, C 4, Q 3, E 2, F 1, R 1, U 1 | 1: U 3 |
H | 11: Q 13, A 5, C 5, E 5, F 5, M 5, U 3, Z 2, B 1, I 1, R 1 | 14: T 11, Q 10, R 8, P 4, U 4, B 3, M 3, W 3, C 2, S 2, D 1, F 1, J 1, Y 1 |
I | 10: Z 4, W 3, A 2, K 2, C 1, F 1, Q 1, R 1, S 1, Y 1 | 11: Q 3, U 3, R 2, S 2, T 2, A 1, F 1, H 1, J 1, M 1, Y 1 |
J | 10: W 4, O 3, C 2, P 2, S 2, H 1, I 1, M 1, T 1, U 1 | 7: S 7, M 5, C 2, F 2, U 2, Q 1, W 1 |
K | 0: — | 1: I 2 |
M | 10: C 8, S 7, J 5, M 4, H 3, Z 2, D 1, I 1, Q 1, R 1 | 8: S 7, C 6, G 5, H 5, M 4, U 2, W 2, J 1 |
Reversals
FS 12 · SF 14HQ 10 · QH 13CT 14 · TC 1CM 8 · MC 6CQ 9 · QC 5MS 7 · SM 7RS 8 · SR 5CF 6 · FC 6AS 4 · SA 7FW 6 · WF 5BS 7 · SB 3QS 9 · SQ 1A
B
Plain
ABCDEFGHIJKLMNOPQRSTUVWXYZThe cipher alphabet must contain exactly 26 letters.