Take the number 192 and multiply it by each of 1, 2, and 3:

    192 × 1 = 192
    192 × 2 = 384
    192 × 3 = 576

By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)

The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product of 9 and (1,2,3,4,5).

What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, ... , n) where n > 1?

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

maxP <- 1
for (i in 1:9999) {
    p <- i
    for (j in 2:9) {
        product <- i * j
        p <- paste(p, product, sep="")
        if (nchar(p)== 9) {
            tmp <- unlist(strsplit(p, split=""))
            if (any(tmp == "0"))
                break
            if (length(unique(tmp)) == length(tmp)) {
                if ( p > maxP) {
                    maxP <- p
                    cat (i ,"\t", j ,"\t", p, "\n")
                }
            }
        } else if (nchar(p) > 9) {
            break
        }
    }
}

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