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 To Know Titans (Posted on 2009-06-14)
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 No Rating

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 computer-aided solution | Comment 1 of 3

A table of factorials from 10 to 16 is:

`10      362880011      3991680012      47900160013      622702080014      8717829120015      130767436800016      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 1320   for Dvr=1234 to 987625    if int(Dvr/10)@10=Ton@10 then30    :Q=!(Ton)//Dvr40    :if Q=int(Q) and Q>99999 and Q<200000 then print Ton,Dvr,Q50   next60   next`

The list produced is:

`12      2520    19008012      3024    15840012      3520    13608012      4224    11340012      4320    11088012      4620    10368012      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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