Split 69 into 3 parts such that they are in arithmetic progression and a product of two smaller parts is 483.

Question

100 coins are lying flat on a table. 10 of them are heads up and 90 are tails up. How can you split the coins into two piles such that there are same number of heads up in each pile?

Answer 1

Factorising 483 gives us 23, 7 and 3 as factors. From this we can see that 23 and (3×7) 21 are also factors.
Now by adding these 2 numbers and subtracting it with 69 gives us 25.
So the number 69 can be split into 21 + 23 + 25 which are in arithmetic progression with 2 as common difference.

Answer 2

21 , 23 , 25