maths puzzle...

[finphoto1972]

There is a six-digit number made up of six different digits which, when multiplied by 2, 3, 4, 5, or 6 returns a six-digit answer which contains exactly the same six digits as the original number but in a different order. And when multiplied by 7 it returns a completely different number which contains none of these digits, which is still quite interesting. What is the original number?

[gardenknowin]

Think you will find that it is 142,857. See "This Book" by Mitchell Symons

[johnalex]

Try this one - Enter 1.2345679 into your calculator, then store in memory. Press the 'C' key which cancels the display to show zero (but retains your magic number in memory). Enter 9 followed by 'x' (multiply) which will simply display 9. Pass the calculator to one of your kids and ask them to enter a whole number between 1 and 9. Then ask them to press 'x' (multiply) followed by MRC (memory recall). Then press = (equals). Their original number is repeated across the screen. Just a bit of Xmas fun!