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 A streetcar named Enigma (Posted on 2010-02-10)
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?

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 computer solution | Comment 2 of 10 |

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  1899019889  1989019979  1998027989  2799028889  2889028979  2898029789  2979029879  2988029969  2997036989  3699037889  3789037979  3798038789  3879038879  3888038969  3897039689  3969039779  3978039869  3987039959  3996045989  4599046889  4689046979  4698047789  4779047879  4788047969  4797048689  4869048779  4878048869  4887048959  4896049589  4959049679  4968049769  4977049859  4986049949  4995054989  5499055889  5589055979  5598056789  5679056879  5688056969  5697057689  5769057779  5778057869  5787057959  5796058589  5859058679  5868058769  5877058859  5886058949  5895059489  5949059579  5958059669  5967059759  5976059849  5985059939  5994063989  6399064889  6489064979  6498065789  6579065879  6588065969  6597066689  6669066779  6678066869  6687066959  6696067589  6759067679  6768067769  6777067859  6786067949  6795068489  6849068579  6858068669  6867068759  6876068849  6885068939  6894069389  6939069479  6948069569  6957069659  6966069749  6975069839  6984069929  6993072989  7299073889  7389073979  7398074789  7479074879  7488074969  7497075689  7569075779  7578075869  7587075959  7596076589  7659076679  7668076769  7677076859  7686076949  7695077489  7749077579  7758077669  7767077759  7776077849  7785077939  7794078389  7839078479  7848078569  7857078659  7866078749  7875078839  7884078929  7893079289  7929079379  7938079469  7947079559  7956079649  7965079739  7974079829  7983079919  7992081989  8199082889  8289082979  8298083789  8379083879  8388083969  8397084689  8469084779  8478084869  8487084959  8496085589  8559085679  8568085769  8577085859  8586085949  8595086489  8649086579  8658086669  8667086759  8676086849  8685086939  8694087389  8739087479  8748087569  8757087659  8766087749  8775087839  8784087929  8793088289  8829088379  8838088469  8847088559  8856088649  8865088739  8874088829  8883088919  8892089189  8919089279  8928089369  8937089459  8946089549  8955089639  8964089729  8973089819  8982089909  8991090989  9099091889  9189091979  9198092789  9279092879  9288092969  9297093689  9369093779  9378093869  9387093959  9396094589  9459094679  9468094769  9477094859  9486094949  9495095489  9549095579  9558095669  9567095759  9576095849  9585095939  9594096389  9639096479  9648096569  9657096659  9666096749  9675096839  9684096929  9693097289  9729097379  9738097469  9747097559  9756097649  9765097739  9774097829  9783097919  9792098189  9819098279  9828098369  9837098459  9846098549  9855098639  9864098729  9873098819  9882098909  9891099089  9909099179  9918099269  9927099359  9936099449  9945099539  9954099629  9963099719  9972099809  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

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