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Powers of 3, 4, and 7 Included (Posted on 2022-01-10) Difficulty: 3 of 5
What is the smallest positive integer N in which you can "see" the consecutive digits of other integers t, f, and s where:

- the digits of N are all unique
- t=i^3, f=j^4, and s=k^7 for some integers i,j,k
- t, f, and s are each at least 3 digits
- there can be overlap of some of the digits of each of the powers as they appear in N.

For example, if N is abcdefg, then a valid solution would be if abcd, cde, and defg were a perfect cube, a 4th power and a 7th power in some order.
Furthermore, if a number's digits are abcd, then it is included in xyabcdz but not included in xabycdz.

See The Solution Submitted by Larry    
Rating: 4.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
A lower numberSteve Herman2022-01-10 12:28:06
Still smaller existsLarry2022-01-10 11:48:07
lower numberCharlie2022-01-10 11:37:04
One NumberH M2022-01-10 09:59:35
Hints/TipsFirst Thoughts (hint)Steve Herman2022-01-10 07:23:08
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