Two years ago, traveling with my friend (a logic wiz) I have purchased two streetcar tickets, consecutively numbered. I told my friend that the sum of all ten digits equals 62, which was his age. He than asked me whether the sum of digits (s.o.d) of either of the tickets equals my age (which he knew) and upon getting my answer quoted exactly both 5-digit numbers.

What were the numbers?
Am I over 50 today?

All but one such pairs of numbers split 27-35 in the sums of digits. However, that one (98999, 99000) has sod's 18 and 44.

So, answering the second question first, you're under 50, as you are one of 18, 27, 35 and 44.

The two numbers are just that pair mentioned above, as it's unique in the pertinent regard: (98999, 99000). If you're 27 or 35 you said that neither sod was your age, narrowing the possibilities down to this pair; if you're 18 or 44, you said, yes, one is the matching age, likewise narrowing it down.

The 27-35 splits come from the following pairs:

18989  18990
19889  19890
19979  19980
27989  27990
28889  28890
28979  28980
29789  29790
29879  29880
29969  29970
36989  36990
37889  37890
37979  37980
38789  38790
38879  38880
38969  38970
39689  39690
39779  39780
39869  39870
39959  39960
45989  45990
46889  46890
46979  46980
47789  47790
47879  47880
47969  47970
48689  48690
48779  48780
48869  48870
48959  48960
49589  49590
49679  49680
49769  49770
49859  49860
49949  49950
54989  54990
55889  55890
55979  55980
56789  56790
56879  56880
56969  56970
57689  57690
57779  57780
57869  57870
57959  57960
58589  58590
58679  58680
58769  58770
58859  58860
58949  58950
59489  59490
59579  59580
59669  59670
59759  59760
59849  59850
59939  59940
63989  63990
64889  64890
64979  64980
65789  65790
65879  65880
65969  65970
66689  66690
66779  66780
66869  66870
66959  66960
67589  67590
67679  67680
67769  67770
67859  67860
67949  67950
68489  68490
68579  68580
68669  68670
68759  68760
68849  68850
68939  68940
69389  69390
69479  69480
69569  69570
69659  69660
69749  69750
69839  69840
69929  69930
72989  72990
73889  73890
73979  73980
74789  74790
74879  74880
74969  74970
75689  75690
75779  75780
75869  75870
75959  75960
76589  76590
76679  76680
76769  76770
76859  76860
76949  76950
77489  77490
77579  77580
77669  77670
77759  77760
77849  77850
77939  77940
78389  78390
78479  78480
78569  78570
78659  78660
78749  78750
78839  78840
78929  78930
79289  79290
79379  79380
79469  79470
79559  79560
79649  79650
79739  79740
79829  79830
79919  79920
81989  81990
82889  82890
82979  82980
83789  83790
83879  83880
83969  83970
84689  84690
84779  84780
84869  84870
84959  84960
85589  85590
85679  85680
85769  85770
85859  85860
85949  85950
86489  86490
86579  86580
86669  86670
86759  86760
86849  86850
86939  86940
87389  87390
87479  87480
87569  87570
87659  87660
87749  87750
87839  87840
87929  87930
88289  88290
88379  88380
88469  88470
88559  88560
88649  88650
88739  88740
88829  88830
88919  88920
89189  89190
89279  89280
89369  89370
89459  89460
89549  89550
89639  89640
89729  89730
89819  89820
89909  89910
90989  90990
91889  91890
91979  91980
92789  92790
92879  92880
92969  92970
93689  93690
93779  93780
93869  93870
93959  93960
94589  94590
94679  94680
94769  94770
94859  94860
94949  94950
95489  95490
95579  95580
95669  95670
95759  95760
95849  95850
95939  95940
96389  96390
96479  96480
96569  96570
96659  96660
96749  96750
96839  96840
96929  96930
97289  97290
97379  97380
97469  97470
97559  97560
97649  97650
97739  97740
97829  97830
97919  97920
98189  98190
98279  98280
98369  98370
98459  98460
98549  98550
98639  98640
98729  98730
98819  98820
98909  98910
99089  99090
99179  99180
99269  99270
99359  99360
99449  99450
99539  99540
99629  99630
99719  99720
99809  99810

DECLARE FUNCTION sod# (x#)
DEFDBL A-Z
OPEN "tktsod.txt" FOR OUTPUT AS #2

FOR n1 = 10000 TO 99998
  n2 = n1 + 1
  s1 = sod(n1): s2 = sod(n2)
  IF s1 + s2 = 62 THEN
   PRINT #2, n1; n2;
   PRINT #2, USING "###"; s1
   PRINT #2, n1; n2;
   PRINT #2, USING "###"; s2
  END IF
NEXT

FUNCTION sod (x)
 s$ = LTRIM$(STR$(x))
 t = 0
 FOR i = 1 TO LEN(s$)
  t = t + VAL(MID$(s$, i, 1))
 NEXT
 sod = t
END FUNCTION

Results were sorted by the individual number sod field.

Posted by Charlie on 2010-02-10 14:13:17