Forum Competition - International Maths Day 2023

[Ravanna]

[Ravanna]

[Argo]

CDV!!

Nice work indeed ..

MIAB has been consulted by a maths consultant and the math consultant said there appears to be a problem with the prime number question .. I dont understand.. but Dez is probably correct ...and I wouldn't know :shrug


Great entries Dejanira and still having a giggle at William Pitts entries - well done and good luck to both of you!

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And so.. on we go_ Here be the next puzzle .... THE THREE-WAY DUELS

Three pirates, Jack, John and Jim, can't agree on how to split the loot from their last pillage, so they decide to have a duel.

The rules are as follows: They draw straws on who will start, and who will go second and third. Then, they take up positions. They each have a gun and an infinite amount of ammunition. The first pirate fires one shot. He can choose whom he will fire at (or he can deliberately miss). Then, it's the second pirate who fires a shot (unless he's dead). Then it's the third pirate's turn (unless he's dead). Then pirate one, then pirate two, then pirate three, then pirate one again, until only one pirate is left alive.



It is common knowledge among Jack, John and Jim that John is a perfect shot; he never misses. It is likewise common knowledge that Jack hits his mark 80% of the time, while Jim only has a 50% chance of hitting what he aims at.

Question A: Given that each pirate chooses the best strategy for themself, who has the highest probability of surviving?

Question B: What is this probability?

GOOD LUCK HAVE FUN!!

[Ravanna]

[Hpwizard]

Who would have thought this would be so easy for you and so hard for me??? Duh!!

max: distance = sqrt(3^2+(3/2)^2) + sqrt((3/2)^2+3^2) = 6.708

rose: Label the 3 directions a,b, and c, where these can refer to any of the side lengths of the rectangular prism. The ant travels an face ab from (0,0,0) to (a, b-x, 0), where x is some positive value less than b. The ant then travels from (a, b-x, 0) to (a,b,c)

distance= sqrt(a^2+(b-x)^2) + sqrt(x^2+c^2)
d/dx (sqrt(a^2+(b-x)^2) + sqrt(x^2+c^2)) = 0 has solutions at x = bc/(c-a) and x = bc/(a+c) --> only the second gives values of 0 < x < b
The total distance traveled for b being each of the 3 sides are:
b=2 -> distance = 7.280
b=3 -> distance = 6.708
b=4 -> distance = 6.403

Final Answer: Rose travels 6.403 units and Max travels 6.708 units. Rose reaches the crumb first.

[Cdv]

And so.. on we go_ Here be the next puzzle .... THE THREE-WAY DUELS

Three pirates, Jack, John and Jim, can't agree on how to split the loot from their last pillage, so they decide to have a duel.

The rules are as follows: They draw straws on who will start, and who will go second and third. Then, they take up positions. They each have a gun and an infinite amount of ammunition. The first pirate fires one shot. He can choose whom he will fire at (or he can deliberately miss). Then, it's the second pirate who fires a shot (unless he's dead). Then it's the third pirate's turn (unless he's dead). Then pirate one, then pirate two, then pirate three, then pirate one again, until only one pirate is left alive.



It is common knowledge among Jack, John and Jim that John is a perfect shot; he never misses. It is likewise common knowledge that Jack hits his mark 80% of the time, while Jim only has a 50% chance of hitting what he aims at.

Question A: Given that each pirate chooses the best strategy for themself, who has the highest probability of surviving?

Question B: What is this probability?

GOOD LUCK HAVE FUN!!

Answer A: Jim
Answer B: approx 44.7%

[Argo]

Well done Ravanna and HP!! Good luck

THE CONSULTANT HAS CONSULTED:


1. Seems like hpwizard got the ant puzzle right.
2. CDV got question A right in the duel puzzle, but he got question B wrong. It's a bit strange that he thinks it's less than 50% when he got A right

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[Argo]

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Not only are you now competing for 50 credits for first place ... 30 for second and 20 for 3rd place from MIAB but
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Send in your entries before reset Wednesdy ... as many as you like ... comment, argue or even perhaps discuss good naturedly each others entries if you don't have a joke or puzzle - to all those that have entered.. Thank you for participating and making this fun and keep em coming -

Good luck Have fun ..

[Cdv]

2. CDV got question A right in the duel puzzle, but he got question B wrong. It's a bit strange that he thinks it's less than 50% when he got A right

Jim, 52.22%

Final Answer: Rose travels 6.403 units and Max travels 6.708 units. Rose reaches the crumb first.

I missed out on that solution. Congrats HP.
(There is an easier way to do that. But then again, it is Math day after all. )