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 Total Toothpaste (Posted on 2004-02-16)
When it's time to squeeze out toothpaste, one method is to press down on one particular "zone" of the toothpaste tube. This way, half of the toothpaste will squirt in each direction except for the zone at the end of the tube. When toothpaste squirts out the zone at the front of the tube, it comes out onto your toothbrush.

The problem is a person who uses this toothpaste-squeezing method has to go in for a dentist visit tomorrow, and he haven't even opened his tube of toothpaste. He figure if he can get 99% of the toothpaste on his toothbrush and brush with it, he will have shiny teeth. It's late at night and he doesn't want to have to squeeze the toothpaste tube more than neccesary.

A) What would be the best squeezing strategy if the tube had 3 zones? 4 zones?

B) Is there a best strategy that could apply for any number of zones?

Example:
`Toothpaste tube-> |4321=`
```1/4, 1/4, 1/4, 1/4, (  0 OUT) Press 3:
3/8,    , 3/8, 1/4, (  0 OUT) Press 1:
3/8,    , 1/2,    , (1/8 OUT) Press 2:
3/8, 1/4,    , 1/4, (1/8 OUT) Press 4:
, 5/8,    , 1/4, (1/8 OUT)```
(Assume any part of the tube can have any amount of toothpaste in it, you can only push in the middle of a zone, and the person will not get sick from toothpaste intake.)

 See The Solution Submitted by Gamer Rating: 4.4000 (5 votes)

 Subject Author Date A thought ronen 2004-02-21 05:36:18 The 4-zone case laid out Charlie 2004-02-17 08:41:23 According to the Colgate University website.... Penny 2004-02-17 07:27:09 Heuristic method Charlie 2004-02-16 15:25:16 lol Tristan 2004-02-16 14:21:41

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