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Enigma 4

15pts

On 1 January 3000, the authorship of Groland have a big party to celebrate the birthday of the oldest inhabitant of Groland, having 100 years old this day. Only Grolandais are invited, but the Palais des Festivals of Groland has a limited number of place. Grolandais are drawn to the entrance on the evening of December 31, 2999 (at exactly midnight).

The draw takes place as follows:

-Once a Grolandais is drawn, his date of birth is written.

-Once a Grolandais is drawn and he has the same date of birth (day, me and year) of an already invited guest (already picked) , the draw is over and he's not invited.

How many guests can the Palais des Festivals receives in maximum ?

Sorry for my poor English

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36,525. 

 

A person can be drawn from age 1 day old to age 100, which is the oldest person. If a person born every single day within that span is drawn before any duplicates, then the following:

 

365 days per year x 100 years = 36,500

Over a 100 year span there would also be 25 leap years, and people who were born on February 29th in leap years could also be selected, adding 25 more potential days to be selected from, and therefore 25 more people that could be selected at maximum.

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Enigma 5

10pts

John wants to buy a chocolate bar for $1 in the distributor. The machine accepts between 5 cent and a dollar (5c, 10c, 20c, 50c and $1), but it does not give back extra money. John doesn't have less then a 5 cent and doesn't have more than a 1$ (in paper or in coin) in his pocket. But, he has more than 1 dollar (total money) in his pocket and it is impossible to give the exact amount of money for this chocolate bar.

How john can have on him up? (The Maximum)

And tell me WHAT he has in his pocket (what cent)

Explain your answer plz

Sorry for my poor English

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