The number 142,857 is in fact an odd number, but it also has some mysterious properties! Multiply it by the numbers 2 to 7 and observe the results. What do you notice? Can you explain the results? Try to find other mysterious numbers that have similar properties.
(Source: Lewis Carroll's Games and Puzzles, Wakeling, E. (Ed.), 1992.)
Submit your idea for an investigation to InterMath.