Mathematical puzzle: ten digit lock number

Question

A mathematical professor set his lock number, he used mathematics so he would remember the ten digit code. He used all of the digits from 0-9, every digit only once. In his mind the first two digits of the code became a two-digit-number (XX). If you multiply this number (by some integer), you get a three-digit-number (YYY), which is formed by the 3rd, 4th and 5th digits of the code. And lastly, if you multiply the first (two-digit-number) with a second (three-digit-number), you get the remaining five digits of the code (five-digit-number).

In other words, we're looking for

XX-YYY-ZZZZZ

where

XX * ? = YYY
XX * YYY = ZZZZZ

And all digits are unique.

Answer 1

Feel a little bit bad because I just brute-forced it but:

27-594-16038

Explanation:

The two digit number is 27. If you multiply this number (specifically by 22) you can get 594. 27 * 594 = 16,038. All these numbers appended together makes 2759416038 which is a ten digit number that uses each digit only once. It is also the only such number that fits all the prescribed rules.

Answer 2

I assumed that "multiply this [two-digit] number" means "multiply it by something unknown" and wrote a simple program to see what this unknown could be. I only found one possible value of this unknown:

The statement will read "multiply this number by 22".

In this case the answer is:

2759416038: 27 * 22 = 594, 27 * 594 = 16038

Answer 3

If I understood the riddle correctly we should find ten numbers (a combination for the lock). The first two numbers form a two digit number which multiplied with it self should form another three digit number. And the two-digit number multiplied with the three digit number should form the full lock combination.

XX^2=XXX

XX*XXX=XXXXX

XX XXX XXXXX = combination key

Answer 4

Checking all possible solutions for this riddle, finally receiving:

XX: 27 , YYY: 594 , ZZZZZ: 16038

x<-0:9
for(i in x){
  for(j in x){
    if(i!=j){
      tmp<-(i*10+j)*1:82
      tmph<-tmp%/%100
      tmpz<-tmp%/%10-10*tmph
      tmpe<-tmp%/%1-100*tmph-10*tmpz
      tmpyyy<-tmp[which(!is.element(tmph,c(i,j)) & !is.element(tmpz,c(i,j)) & !is.element(tmpe,c(i,j)) & tmph!=tmpz & tmph!=tmpe &tmpe!=tmpz & tmp>99 & tmp<1000)]
      tmp<-(i*10+j)*tmpyyy
      tmp2zt<-tmp%/%10000
      tmp2t<-tmp%/%1000-10*tmp2zt
      tmp2h<-tmp%/%100-10*tmp2t-100*tmp2zt
      tmp2z<-tmp%/%10-10*tmp2h-100*tmp2t-1000*tmp2zt
      tmp2e<-tmp%/%1-1000*tmp2t-10000*tmp2zt-100*tmp2h-10*tmp2z
      tmpzzzzz<-tmp[which(!is.element(tmp2zt,c(i,j)) &!is.element(tmp2t,c(i,j)) & !is.element(tmp2h,c(i,j)) & !is.element(tmp2z,c(i,j)) & !is.element(tmp2e,c(i,j)) & tmp2h!=tmp2z & tmp2h!=tmp2e &tmp2e!=tmp2z & tmp2e!=tmp2t &tmp2e!=tmp2zt &tmp2t!=tmp2z&tmp2zt!=tmp2z &tmp2h!=tmp2t &tmp2h!=tmp2zt &tmp2t!=tmp2zt & tmp>9999 & tmp<100000)]
      if(length(tmpyyy)>0 & length(tmpzzzzz)>0){
        for(y in tmpyyy){
          tmph<-y%/%100
          tmpz<-y%/%10-10*tmph
          tmpe<-y%/%1-100*tmph-10*tmpz
          tmp2zt<-tmpzzzzz%/%10000
          tmp2t<-tmpzzzzz%/%1000-10*tmp2zt
          tmp2h<-tmpzzzzz%/%100-10*tmp2t-100*tmp2zt
          tmp2z<-tmpzzzzz%/%10-10*tmp2h-100*tmp2t-1000*tmp2zt
          tmp2e<-tmpzzzzz%/%1-1000*tmp2t-10000*tmp2zt-100*tmp2h-10*tmp2z
          tmpres<-tmpzzzzz[which(!is.element(tmp2zt,c(tmph,tmpz,tmpe))& !is.element(tmp2t,c(tmph,tmpz,tmpe)) & !is.element(tmp2h,c(tmph,tmpz,tmpe))&!is.element(tmp2z,c(tmph,tmpz,tmpe)) & !is.element(tmp2e,c(tmph,tmpz,tmpe))& ((i*10+j)*y==tmpzzzzz))]
          if(length(tmpres)>0){
            cat(paste("XX:",(i*10+j), ", YYY:",y, ", ZZZZZ:",tmpres))
          }
        }
      }
    }
  }
}