For the sequence 1,2,1,2,2,1,2,2,2,1,2,2,2,2,1.................................................................................. the sum of the first n terms is 2018. find n.

How many triples puzzle

How many triples (a; b; c) of positive integers satisfy the conditions 6ab = c^2 and a < b < c 35?

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Question of the day

The natural number n can be replaced by ab if a + b = n, where a and b are natural numbers. How can the number 2001 be obtained from 22 after a sequence of such replacements?


Welcome to Expert Math! Do you have a child who needs a little extra help with high school Math? Or do you want your child to get ahead of the curve? If you want your child to catch up or get ahead, give Expert Math a call! We have a team of Math Experts, each with more than a decade of experience. Our rates are reasonable and become all the more attractive as the group grows. So, if you need a helping hand, don't be afraid to reach out to the Math Experts! We're here to help your child learn and grow. 

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Subjects: Calculus, Vectors, Probability, Advanced Functions

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Question of the day

A man stands in the center of a circle. On the circumference of the circle is a tiger that is constrained to move only around the circle. The tiger can run four times as fast as the man. How can the man escape the circle without being eaten by the tiger? (The tiger will try to minimize its distance from the man at all times)...

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Question of the day - Expert Math club problem

The Expert Math club took a field trip to see the movie MATH IS FUN. 

A total of 27 people went on the trip, including students, teachers, and some parents. 

There were more parents than teachers.

Movie tickets cost $7, but the students got a discount and only had to pay $3 each. 

The group paid a total of $105. 

How many students, teachers, and parents went on the trip?


Welcome to Expert Math! Do you have a child who needs a little extra help with high school Math? Or do you want your child to get ahead of the curve? If you want your child to catch up or get ahead, give Expert Math a call! We have a team of Math Experts, each with more than a decade of experience. Our rates are reasonable and become all the more attractive as the group grows. So, if you need a helping hand, don't be afraid to reach out to the Math Experts! We're here to help your child learn and grow. 

Visit http://www.expertmath.ca

Service offered in: Richmond Hill, Thornhill, North York, Toronto, Markham, Vaughan 
Subjects: Calculus, Vectors, Probability, Advanced Functions

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How many golf balls?

a) How many golf balls can be stacked in a triangular pyramid with a triangular base of ten balls on each side? 

b) How many golf balls can be stacked in a triangular pyramid with a triangular base of n balls on each side? 

How many rectangles are there in an mxn grid?

Let us consider the following grid with m rows and n columns: 

Number of rectangles with dimension 1X1 = m*n

Number of rectangles with dimension 2X1 = (m-1)*n

Number of rectangles with dimension 3X1 = (m-2)*n

....................

Number of rectangles with dimension mX1 = [(m-(m-1)]*n

Similarly,

Number of rectangles with dimension 1X2 = m*(n-1)

Number of rectangles with dimension 2X2 = (m-1)*(n-1)

Number of rectangles with dimension 3X2 = (m-2)*(n-1)

..............

Number of rectangles with dimension mX2 = [(m-(m-1)]*(n-1)

Increasing the number of columns incrementally by 1, the last set of number of rectangles with n columns are

Number of rectangles with dimension 1Xn = m*1

Number of rectangles with dimension 2Xn = (m-1)*1

Number of rectangles with dimension 3Xn = (m-2)*1

.....................

Number of rectangles with dimension mXn = [(m-(m-1)]*1

Sum (1X1, 2X1, 3X1…..mX1) = n * [m + (m-1) + (m-2) +……1]                = n * m(m+1)/2

Sum (1X2, 2X2, 3X2…..mX2) = (n-1) * [m + (m-1) + (m-2) +……1]         = (n-1) * m(m+1)/2

Sum (1X3, 2X3, 3X3…..mX3) = (n-2) * [m + (m-1) + (m-2) +……1]         = (n-2) * m(m+1)/2

.....................

Sum (1Xn, 2Xn, 3Xn…..mXn) = [(n-(n-1)] * [m + (m-1) + (m-2) +……1]  = 1 * m(m+1)/2

And total number of rectangles will be sum of the sums of rectangles of various sizes

So, S = [m(m+1)/2] * [n + (n-1) + (n-2) +…….1]

S = [m(m+1)/2] * S = [n(n+1)/2]

S = mn(m+1)(n+1)/4

Welcome to Expert Math! Do you have a child who needs a little extra help with high school Math? Or do you want your child to get ahead of the curve? If you want your child to catch up or get ahead, give Expert Math a call! We have a team of Math Experts, each with more than a decade of experience. Our rates are reasonable and become all the more attractive as the group grows. So, if you need a helping hand, don't be afraid to reach out to the Math Experts! We're here to help your child learn and grow. 

Visit http://www.expertmath.ca

Service offered in: Richmond Hill, Thornhill, North York, Toronto, Markham, Vaughan

Subjects: Calculus, Vectors, Probability, Advanced Functions
Specialized tutoring in IB Mathematics, AP Mathematics, Academic Mathematics, Applied Mathematics