INTRODUCTION
I also have a few new photographs to share, but the main purpose of this post is to answer the question I included in “Midweek Medley“.
THE ANSWER
There are three elements to this section – first a screenshot showing the correct answer, then my written explanation of how I worked it out (I did it in my head in rather less time than the explanation takes) and then another screenshot showing a solution posted on brilliant.
I solved this one as follows:
Firstly I noted that the smallest base that need be considered is base 8. Then I converted 777 from bases going upward from 8 back into base 10 and assessed whether or not the number was a fourth power.
777 in base 8 is 511 in base 10 = 73 x 7 = not a fourth power.
777 in base 9 is 637 in base 10 = 91 x 7 = not a fourth power.
777 is not a fourth power
777 in base 11 is 931 in base 10 = 133 x 7 = 49 x 19 = not a fourth power
777 in base 12 is 1099 in base 10 = 157 x 7 = not a fourth power.
777 in base 13 is 1281 in base 10 = 183 x 7 = 61 x 7 x 3 = not a fourth power
777 in base 14 is 1477 in base 10 = 211 x 7 = not a fourth power
777 in base 15 is 1687 in base 10 = 241 x 7 = not a fourth power
777 in base 16 is 1911 in base 10 = 273 x 7 = 39 x 7 x 7 = 39 x 49 = 3 x 13 x 7 x 7 = not a fourth power.
777 in base 17 is 2149 in base 10 = 307 x 7
777 in base 18 is 2401 in base 10 = 343 x 7 = 49 x 7 x 7 = 7 x 7 x 7 x 7 = 7^4 = a fourth power.
Thus the answer is indeed 18.
Below is a screenshot of Jerry Han Jia Tao’s solution posted on brilliant:
Rather more elegant than my method of solving by brute calculation – but it was early in the morning when I tackled this problem, which is possibly why I missed this approach.
A NEW PROBLEM
This was the one I solved this morning to extend my solving sequence on brilliant to 252 days:
PHOTOGRAPHY
aspiblog 