In the land of Binaria, the currency consists of coins worth 1¢ , 2¢ , 4¢ , 8¢ , 16¢ , 32¢ and 64¢ . Bina has two of each coin. How many combinations of her coins have a combined value of 50¢ ?

me personally i just brute forced it but it didnt work

cheeeeeeese May 28, 2024

#1**0 **

We can solve this by realizing that 50¢ can be represented as the sum of 32¢ and 18¢.

For the 32¢ portion, Bina has two 32¢ coins, so there's only 1 choice (use both 32¢ coins).

For the remaining 18¢, Bina can use:

One 16¢ coin and one 2¢ coin (2 choices)

Two 8¢ coins (1 choice)

Nine 2¢ coins (1 choice)

So in total, there are 1 (32¢) + 2 (16¢+2¢) + 1 (8¢+8¢) + 1 (2¢+2¢+...+2¢) = 5 different combinations that add up to 50¢.

bader May 28, 2024