Does anyone know any good maths puzzles to give to an A-Level group??
Get them to solve this:
GAMESHOW PROBLEM
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?
Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?
This is a well documented problem documented in many books and on the internet and often fools the most intelligent of mathematicians. Quite interesting though.
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Why is this not true
let a = b
multiply by a
a^2 = ab
subtract b^2
a^2 – b^2 = ab – b^2
factor
(a+b) (a-b) = b(a-b)
divide by a-b
a + b = b
but a = b so
b + b =b
and
2 = 1
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Answer this.
In a pond there are some flowers. Few birds came there. If each bird sit in each flower, one bird will not get any flower. If two birds sit on one flower one flower will be empty.
How many birds? and how many flowers?
References :
we offer flowers to 12 children meeting them one by one and giving half of the flowers each time and take back only one from those given to the child. if the 12th child was given only one flower, how many flowers we had in the beginning? Find.
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Study successive differences in a few of the series f(n) = n^a where 'a' is a positive integer not more than 5.how does final difference relate to 'a'.Does same hold for slghtly altered expression such as f(n)=2n^a + n^(a-1), any similar variations.
References :
Get them to solve this:
GAMESHOW PROBLEM
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?
Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?
This is a well documented problem documented in many books and on the internet and often fools the most intelligent of mathematicians. Quite interesting though.
References :