perplexus.info :: Numbers : Erasing digits

Erasing digits (Posted on 2002-04-27)

Digits from 1 to 9 are written on the board.

A student erases a few of them, and instead writes the digit(s) of their product. (For example if he erases 4, 3 and 7 he would write the digits 8 and 4 since 4 * 3 * 7 = 84.) He also writes a few other random digits on the board.

He repeats this process until only one digit remains on the board. What is this digit and why?

Submitted by levik

Rating: 2.9091 (11 votes)

Solution: (Hide)

The last digit left will be zero.
The digits initially on the board include a "5", which will result in either another 5 when multiplied by an odd digit, or in a 0 if multiplied by an even one.
Once a zero appears on the board, it is impossible to erase by these rules, since multiplying anything by zero still results in a zero.
Therefore, if there is only one number remaining, zero is it.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2022-05-09 21:25:57
the digit	Math Man	2012-09-27 20:12:23
Solution	Lisa	2005-05-10 15:19:48
well,	Jonathan Waltz	2003-03-31 08:55:08
answer	Erin	2003-01-14 09:14:01
re: i have to disagree	cges	2002-12-11 06:24:21
re: i have to disagree	friedlinguini	2002-12-10 06:14:10
i have to disagree	Cory Taylor	2002-12-10 04:28:11
Solution	cges	2002-12-09 06:00:01
My Answer	Tom	2002-05-09 12:52:41

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