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Mathematics-Online problems: | ||

## Solution to the problem of the (previous) week |

** Problem:**

- The contents of the bottles are mixed by completely filling up one of the partly filled bottles from one of the other two bottles. What are the possible alcohol contents of a full bottle after one or two acts of decanting?
- What is the alcohol content when mixing the liquid of all three bottles?

**Answer:**

- Possible alcohol contents after one or two acts of decanting:
< < < < <

- Total alcohol content:

(All results in % and ascending order.)

** Solution:**

- Let be the alcohol contents of the bottles filled
to 1/3, 2/3, and completely. Then, after one
act of decanting, there are three
possibilities for the alcohol contents :
- Filling up the bottle of
1/3 content from the bottle of 2/3 content (or vice versa):
- Filling up the bottle of
1/3 content from the full bottle:
- Filling up the bottle of
2/3 content from the completely full bottle:

The possible alcohol contents of full bottles,

- Filling up the bottle of
1/3 content from the bottle of 2/3 content (or vice versa):
- If we mix two full bottles obtained by decanting, the total
alcohol content is

[problem of the week]