A Method to count: Assume first that the smallest triangles are of a unit length. Note that every possible triangle are equilateral. Now, count as follows: (i) How many triangles are of a unit length? 9 unit-length triangles (ii) How many triangles are of two unit lengths? 3 two-unit-length triangles (iii) How many triangles...

(Both the question & a possible solution may be found in the images below)

What’s the Pattern? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Construction of a building is planned to be completed in 22 days if done by 20 persons. After 10 days’ work, it is terminated for five days. In order for the building to be completed on time, (how many) additional workers are needed? A) 40 B) 30 C) 25 D) 20 Solution: Please see...

2,520 is the “smallest” number which is divisible by “all” numbers from 1 to 10. How? Why? LCM = Least Common Multiple So, LCM (1,2,3,4,5,6,7,8,9,10) = 5 x 7 x 2^3 x 3^2 = 5 x 7 x 8 x 9 = (8 x 5) x (9 x 7) = 40 x 63 =...

Find all positive integers m such that m weeks = n! seconds

Biblical-Theology, Music & Math (in that order from “most” to “least”)

 

  I think it’s like this (I could be wrong): Let t = time taken by the “blue” car when the two cars meet (in hours). And, d = distance travelled by both cars when they meet (in km). So, the invariant here is “d”. Thus since Distance = Velocity x Time, We have...

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