Some maths brain teasers qns
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Since everyone is bored, I shall give some qns from my sec school maths olympiads. Dun worry as this qn is not about something that we have not learnt. The qn is more about identifying patterns and using this to solve it.
A pattern of triangles is made from matches as shown above.
If there are 107 matches used, how many triangles have been formed? -
52 or 53?
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53 ?
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(107-3)/4 * 2 + 1 = 53Originally posted by tanjun:Since everyone is bored, I shall give some qns from my sec school maths olympiads. Dun worry as this qn is not about something that we have not learnt. The qn is more about identifying patterns and using this to solve it.
A pattern of triangles is made from matches as shown above.
If there are 107 matches used, how many triangles have been formed? -
No. of matchsticks required to form first triangle = 3
=> No. of matchsticks left = 104
Subsequently, no. of matchsticks required to form a triangle = 2
=> No. of subsequent triangles formed = 104/2 = 52
Total no. of triangles formed = 52 + 1 = 53 -
find
sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*..........to infinity
P.S. sry lazy to post square root graphic out -
Write 0.3 + 0.03 + 0.003 + ... (to infinity) as a fraction in its lowest terms.
Anyone can enlighten me on the approach to solve this question? -
it is a finite GPOriginally posted by shagadelic1892:Write 0.3 + 0.03 + 0.003 + ... (to infinity) as a fraction in its lowest terms.
Anyone can enlighten me on the approach to solve this question?
first term, a= 0.3
r is 0.1
so the sum to infinity is
a / (1-r) = 0.3 / 0.9 = 1/3
if you press calculator, 1/3 is 0.3333333333333333333333333333
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ahh.....geometric progression....never thought of that.
it is a finite GP
first term, a= 0.3
r is 0.1
so the sum to infinity is
a / (1-r) = 0.3 / 0.9 = 1/3
if you press calculator, 1/3 is 0.3333333333333333333333333333
As for my solution, it's rather straightforward:
0.3 + 0.03 + 0.003 + .... = 0.333333333..... = 1/3
Thanks for showing me a more proper way of solving this!
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Matchsticks = 2n+1
n=(Matchsticks -1) divide 2
(107-1)/2=53? -
53. You see ar....
.....
...
= 53 -
Yup. The answer is 53. Congrats to all those who got it.Originally posted by tanjun:Since everyone is bored, I shall give some qns from my sec school maths olympiads. Dun worry as this qn is not about something that we have not learnt. The qn is more about identifying patterns and using this to solve it.
A pattern of triangles is made from matches as shown above.
If there are 107 matches used, how many triangles have been formed?
First triangle needs 3 matches. Subsequent triangles form require only 2 matches.
(107 - 3) = 104 matches left to form the rest of triangles
No. of triangles formed = 104/2 + 1
= 53 -
Answer is 2.Originally posted by eagle:find
sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*..........to infinity
P.S. sry lazy to post square root graphic out
If u work out and put the reaulting ans in indices form,
First term = 2^1/2
Second term = 2^3/4
Third term = 2^7/8
and so on and so forth
Basically, u wish to find up till infinity.
Notice that the pattern lies in the powers of 2.
1/2, 3/4, 7/8, 15/16, 31/32 and so on and so forth.
Notice the difference between the terms and rephrase the series accordingly.
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... to infinity
Hence, it is a GP similar to a qn above.
a = 1/2
r = 1/2
Using formula of GP for sum to infinity when r < 1,
Sum to infinty = a/(1-r)
= 0.5(1-0.5)
= 1
What does this mean?
This means that
First term = 2^1/2
Second term = 2^3/4
Hence, following the above series to infinity,
ans will be 2^1 = 2 -
Another brain teaser qn,
If 50 workers can build 20 chairs in 8 days, then how many days do 10 workers need to build 10 chairs, given that all the workers work at the same rate? -
10 day - 10 worker - 5 chairs? -
No. of days required for 50 workers to build 20 chairs = 8Originally posted by tanjun:If 50 workers can build 20 chairs in 8 days, then how many days do 10 workers need to build 10 chairs, given that all the workers work at the same rate?
No. of days required for 50 workers to build 10 chairs = 4 (since workload is halved)
Assuming 10 workers work exactly 5 times slower than 50 workers,
=> No. of days required for 10 workers to build 10 chairs = 4 x 5 = 20
Work with one variable at a time. Correct? -
That's quite a nice way of solving...Originally posted by tanjun:Answer is 2.
If u work out and put the reaulting ans in indices form,
First term = 2^1/2
Second term = 2^3/4
Third term = 2^7/8
and so on and so forth
Basically, u wish to find up till infinity.
Notice that the pattern lies in the powers of 2.
1/2, 3/4, 7/8, 15/16, 31/32 and so on and so forth.
Notice the difference between the terms and rephrase the series accordingly.
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... to infinity
Hence, it is a GP similar to a qn above.
a = 1/2
r = 1/2
Using formula of GP for sum to infinity when r < 1,
Sum to infinty = a/(1-r)
= 0.5(1-0.5)
= 1
What does this mean?
This means that
First term = 2^1/2
Second term = 2^3/4
Hence, following the above series to infinity,
ans will be 2^1 = 2
Alternatively, you can do this
let y = sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*..........
hence y^2 = 2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*sqrt(2*..........
Thus, we can see that
y^2 = 2y
y^2 - 2y = 0
solving gives y = 0 (reject) or y = 2 (answer) -
Isn't this a normal e maths question?Originally posted by tanjun:Another brain teaser qn,
If 50 workers can build 20 chairs in 8 days, then how many days do 10 workers need to build 10 chairs, given that all the workers work at the same rate?
50 workers make 20 chairs in 8 days
10 workers make 4 chairs in 8 days
10 workers make 2 chairs in 4 days
10 workers make 10 chairs in 20 days
answer 20 days -
i think is 5 days
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Another cheap-labour question but slightly more difficult
A and B working together can complete a job in 10 days. B and C working together can complete the job in 15 days. A and C working together can complete the job in 12 days. How many days would it take A, B and C working together to complete the job? -
use bulldoze method mah...Originally posted by shagadelic1892:Another cheap-labour question but slightly more difficult
A and B working together can complete a job in 10 days. B and C working together can complete the job in 15 days. A and C working together can complete the job in 12 days. How many days would it take A, B and C working together to complete the job?
A and B complete 18 jobs in 180 days
B and C complete 12 jobs in 180 days
A and C complete 15 jobs in 180 days
A B and C complete (18+12+15)/2 jobs in 180 days
A B and C complete 22.5 jobs in 180 days
A B and C complete a job in 180/22.5 days
A B and C complete a job in 8 days -
Yes. A very common E maths question.Originally posted by eagle:Isn't this a normal e maths question?
50 workers make 20 chairs in 8 days
10 workers make 4 chairs in 8 days
10 workers make 2 chairs in 4 days
10 workers make 10 chairs in 20 days
answer 20 days
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Yup. Congrats to those who has gotton the answer. The answer is 20.Originally posted by tanjun:Another brain teaser qn,
If 50 workers can build 20 chairs in 8 days, then how many days do 10 workers need to build 10 chairs, given that all the workers work at the same rate? -
I have another method but as usual slightly longer than eagle one.Originally posted by shagadelic1892:Another cheap-labour question but slightly more difficult
A and B working together can complete a job in 10 days. B and C working together can complete the job in 15 days. A and C working together can complete the job in 12 days. How many days would it take A, B and C working together to complete the job?
My method is to use productivity to solve it.
Let a be the productivity of A
Let b be the productivity of B.
Let c be the productivity of C.
(a + b)(10) = 1 (1 job so equal to 1)
(b + c)(12) = 1
(a + c)(15) = 1
a + b = 1/10 --------------(1)
b + c = 1/12 ---------------(2)
a + c = 1/15 ---------------(3)
Taking (1) - (2)
a + b - b - c = 1/10 - 1/12
a - c = 1/60 ----------------- (4)
(1) + (4)
2a = 1/15 + 1/60
2a = 1/12
a = 1/24
From (1)
b = 1/10 - 1/24
= 7/120
From (3)
c = 1/40
Let the No of days that A and B and C work together to complete the job be d.
(a + b + c)(d) = 1
(1/24 + 7/120 + 1/40)(d) = 1
(1 /8 )(d) = 1
d = 8
Is that correct? -
Wah, this is a nice thread, I got a teaser question, sounds very simple but is actually very tricky lor...
There are 2 pair of couples sitting on a bench in a park, how many unique photos can they take assuming each unique photo show the 2 couples sitting in different position and the fact that the couples do not wish to be seperated from their boyfriend/girlfriend?