Math Riddle – 1
A 26″ x 26″ square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 27 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?
What if the metal plate is in the shape of a regular polygon (e.g., pentagon, hexagon, heptagon, octagon, etc.)? Try generalizing the above result to the case of a regular polygon.
Math Riddle – 2
A painting job can be completed by 5 painters in 37 days. If 10 more painters join the team 7 days after starting work on the job, then how many more days are required to complete the job?
The number of days for the job is inversely proportional to the number of painters. So, is ‘number of days × number of painters = constant’?
What assumptions were made to arrive at the solution?
Is something assumed about the output of the painters?