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To Know Titans (Posted on 2009-06-14) Difficulty: 2 of 5
Solve this alphametic, where each of the capital letters in bold represents a different decimal digit from 0 to 9. None of the numbers contains any leading zero.

(TO)! = (KNOW)*(TITANS)

See The Solution Submitted by K Sengupta    
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Solution computer-aided solution | Comment 1 of 3

A table of factorials from 10 to 16 is:

10      3628800
11      39916800
12      479001600
13      6227020800
14      87178291200
15      1307674368000
16      20922789888000

(TO)! should come out to nine or ten digits so as to be the product of a four-digit number times a six-digit number, so TO is either 12 or 13.

The following program merely checks possible four-digit divisors of TO! where the third digit matches the units digit of TO and the quotient has six digits starting with a 1. Variable Ton is used for TO, as TO is a reserved word.

10   for Ton=12 to 13
20   for Dvr=1234 to 9876
25    if int(Dvr/10)@10=Ton@10 then
30    :Q=!(Ton)//Dvr
40    :if Q=int(Q) and Q>99999 and Q<200000 then print Ton,Dvr,Q
50   next
60   next

The list produced is:

12      2520    190080
12      3024    158400
12      3520    136080
12      4224    113400
12      4320    110880
12      4620    103680
12      4725    101376

of which only the last row fits the pattern:

12! = 4725 * 101376


  Posted by Charlie on 2009-06-14 13:22:55
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