More puzzle than joke

[polycrac]

I had to devise and read out a puzzle for the radio today. They put the puzzle on their website (https://www.bbc.co.uk/programmes/articles/4MyyHRb7fh78GP1Q78sY71S/today-puzzle-671) today with the answers tomorrow, but I thought I'd treat you to an early view:

Robin Hood is showing off his skills. He shoots an arrow North, trying for the Sherwood Forest distance record. This arrow has a rubber head and bounces twice when fired. Each time it bounces, it goes off in a random direction (North, South, East or West). The current distance record is set at 99m North of Robin. If Robin’s first shot goes 70m, the first rebound 50m and the second rebound 30m, what is the chance the arrow will finish further North than the record? What is the chance the arrow will end up behind Robin?

Spoiler: Answer below

To break the record, Robin needs either of the bounces to go North, and none of the bounces to go South. The chance of this is 31.25%. The only way the arrow could end up behind him is if both bounces move the arrow South, the chance of this is just 6.25%. You can find these answers using a probability tree, counting how far North the arrow travels in every case:

First shot​	First rebound​	Second rebound​	Record winner?​	Behind Robin?​
70​	N=120​	N=150​	y​	0​
		E=120​	y​	0​
		W=120​	y​	0​
		S=90​	0​	0​
	E=70​	N=100​	y​	0​
		E=70​	0​	0​
		W=70​	0​	0​
		S=40​	0​	0​
	W=70​	N=100​	y​	0​
		E=70​	0​	0​
		W=70​	0​	0​
		S=40​	0​	0​
	S=20​	N=50​	0​	0​
		E=20​	0​	0​
		W=20​	0​	0​
		S=-10​	0​	1​
			(5/16)​	(1/16)​
			0.3125​	0.0625​

 

[Scott]

I love puzzles...... I'll be back

 

[ubuysa]

But my Robin is standing on the North Pole and so he can't shoot an arrow North.......

(And you didn't say he was actually IN Sherwood Forest).

 

[Scott]

Spoiler

70 - 50 - 30

4 options in a combination of 2 = 4 squared (16)

Behind can only happen in one scenario, double bounce south which means 1 in 16

Record can happen if the 1st or 2nd bounce moves north with either of the others moving east or west. There are 6 northern movements possible but one includes south which can be discounted

Winning combos are:

North North
North West
North East
East North
West North

5 in 16

 

[polycrac]

(And you didn't say he was actually IN Sherwood Forest).

True, could just be the sponsor the contest - I need to tighten that wording!

 

[Bradden]

Awesome.. i heard that on the radio this morning.. i love your puzzles. [emoji16]

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