Brain teaser

[J_V]

Here's a brain teaser, I'm struggling with:


During my vacation last summer it rained on 13 days. But when it rained in the morning, the afternoon was dry. Also every rainy afternoon was preceded by dry morning. There were 11 dry mornings and 12 dry afternoons. How many days long was my vacation?


If anyone cares to help me that would be great.

[-Skeme-]

<font color="white">
There are three possible states for each entire day:

1) Clear Morning, Clear Afternoon (x)
2) Rainy Morning, Clear Afternoon (y)
3) Clear Morning, Rainy Afternoon (z)

If it rained on 13 days, then
RMCA (y) + CMRA (z) = 13
If there were exactly 11 nice mornings then.
CMCA (x) + CMRA (z) = 11
If there were exactly 12 nice afternoons then,
CMCA (x) + RMCA (y) = 12

As there were more Clear Afternoons than Clear Mornings, then
CMCA(x)+RMCA(y) &gt; CMCA(x) + CMRA(z)
Therefore:
RMCA (y) &gt; CMRA(z)

By progression from:
x + y = 12
x + z = 11
y + z = 13
and y &gt; Z

the only numbers that fulfill all three requirements are

5 Clear Mornings, Clear Afternoons (x)
7 Rainy Mornings, Clear Afternoons (y)
6 Clear Mornings, Rainy Afternoons (z)

For a total of 18 days.
</font>

[partygirluk]

OK rain on 13 days.

One more dry morning than dry afternoon. Therefore one more were afternoon than wet morning. Therefore 7 wet afternoons, 6 wet mornings. Plus 5 fully dry days. So 18 day holiday /images/graemlins/grin.gif

[J_V]

Damn that is fast guys.

[cnfuzzd]

[ QUOTE ]
Here's a brain teaser, I'm struggling with:


During my vacation last summer it rained on 13 days. But when it rained in the morning, the afternoon was dry. Also every rainy afternoon was preceded by dry morning. There were 11 dry mornings and 12 dry afternoons. How many days long was my vacation?


If anyone cares to help me that would be great.

[/ QUOTE ]

not long enough?

peace

john nickle

[J_V]

[ QUOTE ]
Plus 5 fully dry days.


[/ QUOTE ]

Where does this come from?

[namknils]

Wow

[mmbt0ne]

You give 23 dry halfdays. We know that 13 of those had rain on the other half, so now we have 10 halfdays, for 5 more days.

18.

[-Skeme-]

LOL. I Googled, fools. I couldn't work those problems out if my life depended on it. I have probably 5th grade math skills. Seriously.

[TheWorstPlayer]

Well you know that the days that it didn't rain had both a dry morning AND a dry afternoon and it doesn't matter whether it rains in the morning or afternoon, it only matters that it can't rain in both so each rainy day has to take one from either a morning or an afternoon but not both. So if the number of dry days is X then you know that the number of morning where it rained, plus the number of afternoons where it rained, has to equal 13 or in notation: (12-X)+(11-X)=13. Which gives you 23-2X=13 -&gt; 2X=10 -&gt;X=5. So you know that there are five dry days and it told you that there were 13 rainy days, so that means the vacation was 18 days.

[kyro]

Another way if you care. V = AR + AD = MR + MD. AD = 12, MD = 11. AR + MR = 13. 2V = AR + AD + MR + MD = 36. V = 18.

[RacersEdge]

x=rainy morning days
y=rainy afternoon days
z=no rain days

x+z=12
y+z=11
x+y=13

Solve.