An unknown route with a MAP invites an INROAD from many an IMP.
Now MAP * IMP = INROAD if the following conditions are met:
1. The two multipliers are semiprimes.
2. Each of the 4-digit partial products are a pair of consecutive integers with a difference equal to their multiplying digit.
Determine the 4 primes which form the original multipliers.
The alphametic does have two solutions but the second does not meet the given criteria. Identify why.
The alphametic does have two solutions:
Only the second meets both criteria :
1.Both multiplicand 807 (3*269 ) and multiplier 287 (7*41) are semi-primes.
2. Since there is a difference of 1 between the number of hundreds and the number of units and there is 0 tens in 807 all partial products will consist of concatenation of two 2-digit numbers differing by 1 times the according multiplier's digit: 16-14=2; 64-56=8 and 56-49=7.
No need to check the 1st (a) triplet; it will not work.
So 807*287=231609 is the true solution, although labeled 2nd
by the solver and 1st by the author.