Quizzes & Puzzles1 min ago
number puzzle
i am thinking of a six digit number between 100000 and 200000. if you shift the last three digits and put them in the same order in front of the first three you get exactly six times the original number
what number am i thinking of
Answers
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For more on marking an answer as the "Best Answer", please visit our FAQ.Solution: If the first three numbers are represented by x, where x lies between 100 and 999, and the second three numbers are represented by y, then the original number is 1000x + y.
Since 6(1000x + y) = 1000y + x (the triples switch)
Then 5999x = 994y
Factorising 7.857x = 2.7.71y
Cancelling the 7's, we see that equality is possible only if x = 2.71 = 142 and y = 857 (which is prime)
Hence the original number must be 142,857.
I left the posting to you as promised, crofter, but can't resist having my twopennorth. I got the answer by trial and error arithmetic only but, following on from NILYA's posting, the first number is one seventh and the second is six sevenths of a whole. Thus it was only a case of dividing one by seven to get the first number and six by seven to get the second number then rounding both down to six decimal places. Amazing how things are always obvious with hindsight:-)
Evening, bobobalde111, and thanks for the usual Tuesday entertainment. It (almost) makes it worth dragging myself into work for.