A. 512. We have coins, each one indistinguishable from the other in terms of size and appearance, but only n-1 of them have the same weight, whilst one of them is a counterfeit, being either lighter or heavier than the rest. Using a balance we have to find the counterfeit coin. Show that by k measurements it is possible to find the counterfeit coin and to determine whether it is heavier or lighter than the rest; moreover, it is possible to arrange the measurements in advance, without knowing the results of the measurements.
K. 256. In a three-digit number, the digit in the ones' place is 3 smaller than the digit in the hundreds' place.
a) Find the largest number that meets the condition.
b) How many such numbers are there altogether?
c) Find all numbers that meet the above condition, for which by subtracting the number obtained by reversing the order of the digits the result is 297.
This problem is for grade 9 students only.
Solution (in Hungarian)