Dancing with digits
Number Theory
Level
3
4 random digits when arranged in all possibilities without repeating will add up to 166650. What are the 4 digits? PS. there could be more than one set of answer, but you have to choose from the options. Discussions are most welcomed!
4,5,7,9
2,3,4,5
5,6,8,9
2,3,7,9
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1 solution
let's assume four digits to be k,l,m,n if we sum up all combinations of this four digits, there are actually 24 combinations which are: klmn,klnm,kmln,kmnl,knlm,knml, lkmn,lknm,lmkn,lmnk,lnkm,lnmk, mkln,mknl,mlkn,mlnk,mnkl,mnlk, nklm,nkml,nlkm,nlmk,nmkl,nmlk
You can notice that, if you sum up all the values, there are actually 6(k000)+6(k00)+6(k0)+6(k)+6(l000)+6(l00)+6(l0)+6(l)....6(n) By knowing so, we can conclude that,
6(kkkk)+6(llll)+6(mmmm)+6(nnnn)=166650
6(1111)(k+l+m+n)=166650 k+l+m+n=25
therefore, whatever four digits sum up together which result 25 will fulfill the requirement. From the options, 4+5+7+9=25 (correct answer)