The answer is given at once by converting 1,000,000 to the Septenary scale, and it is on this subject of scales of notation that I propose to write a few words for the benefit of those who have never sufficiently considered the matter.
"Amusements in Mathematics"
Henry Ernest Dudeney
Keep on dividing this number by 7 until there is nothing more left to divide, and the remainders will be found to be 11333311 which is 1,000,000 expressed in the Septenary scale.
"Amusements in Mathematics"
Henry Ernest Dudeney
It is thus seen that no "trials" are necessary; by converting to the Septenary scale of notation we go direct to the answer.
"Amusements in Mathematics"
Henry Ernest Dudeney