Fossils

To ‘fossilise’ a number, you just multiply its digits together. Then do the same with the result, repeating the process until the number remaining has only one digit.

If this digit is zero, we say that the number leaves no fossil.

For example,             489 gives 4 x 8 x 9    = 288

288 gives 2 x 8 x 8    = 128

128 gives 1 x 2 x 8    =  16

16 gives   1 x 6          =    6.

 So, we say that 489 leaves a fossil of 6.

The Problems:

 1.    Find a number with 5 digits that leaves a fossil of 6. Too easy?

        If all the original digits have to be different, can you find one?

2.    What is the largest 3-digit number that leaves a fossil of 4?

3.    Find the largest number whose digits are all different, that leaves a fossil.

4.    Find the largest number, whose digits are all different, that leaves an odd number for a fossil.

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Last modified: June 18, 2007