For Students

 

Spotlight problem!

 

A painter, standing on a rung of a ladder, notices that there are as many rungs below the rung she is standing on as above it. After descending eight rungs she notices that the number of rungs below and above the rung she is on are equal. The number of rungs on the ladder is?

 
 

Send your solutions (you must show your work) to problems@amt.edu.au or post them to our Facebook wall.

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Previous problem

 

In how many ways can 27 be written as the sum of two primes?

 
 

The solution

 

We know that (odd number)+(even number) always, no matter what, equals an odd number.

Since all even numbers apart from 2 are composite, There are only one solution left.

Quick calculations show that 27-2=25 and 25 is NOT a prime number.

Therefore, 27 cannot be written as a sum of 2 primes no matter what.

 

Congratulations to Leon Shinka for the first correct solution! And to the many others who sent in a correct solution.