number puzzle

[bobobalde111]

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

[crofter]

The number is 142857

Note: 6 x 142857 = 857142

[crofter]

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.

[NILYA]

It is also interesting to note that the same six figures come up in different order, as decimals of 1/7, 2/7, etc.

[juliefer]

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.

[bobobalde111]

many thanks as ever

im going on holiday next week (still in scotland) so will try and post question whereever i find a computer

[crofter]

bob Thanks for the Tuesday puzzle and julifer Thanks for the chance of first bite. Last week, I thought you were joking!

[juliefer]

Have a good holiday.

[bobobalde111]

i reckon thats the hardest puzzle for quite a while