perplexus.info :: Numbers : Traveller's Woe

Traveller's Woe (Posted on 2013-11-05)

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.

Bonus Challenge:
The alphametic does have two solutions but the second does not meet the given criteria. Identify why.

See The Solution Submitted by brianjn

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answer + comments - spoiler

| Comment 1 of 2

The alphametic does have two solutions:

a. 857*187=160259

b. 807*287=231609

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.

Posted by Ady TZIDON on 2013-11-05 15:27:24

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