Since last August, I have been very happy and grateful for getting to work on Mathematics with wonderful students in a beautiful new school. Isabelle is one who loves to sketch creative drawings when she finishes Maths tests early with some minutes to spare. Today, I will feature a brainteaser about the following picture.
BRAINTEASER INSPIRED BY ISABELLE’S DRAWING
Isabelle used a free page from her school diary, but the drawing was actually made exactly 2n weeks after the date shown on the page, where the exponent n is the largest whole number that is possible to-date.
Your fun challenge is to figure out the value of n, and the precise date on which Isabelle actually drew her drawing.
A solution will be posted in April.
In the meantime, I wish everyone a wonderful weekend now, bringing happiness to others too.
Solution to brainteaser in Blog Post #52
The challenge was to find the maximum number of consecutive positive whole numbers which, when all added together, produce a total sum of exactly 15219.
OK, a standard formula for the sum of the first n natural numbers is S=n(n+1)/2, and so 2S=n(n+1). Therefore, n will be slightly less than the square root of 2S. Now, √(2×15219) is roughly 174.5, which suggests trying 174 for n. In that case, n(n+1)/2=174×175/2=15225, which only very slightly overshoots 15219 by six. Since 1+2+3=6, our sum 1+2+3+…+172+173+174 will be exactly right if we trim it to 4+5+6+…+172+173+174=15219. That is the optimal sum of 171 consecutive positive whole numbers for getting a total of 15219.