Problem
COM-B1-M06-P008 Fifteen Coins
#8
★★☆☆☆ Level 2 of 5
There are \(15\) coins heads up. In one move, any \(4\) coins are flipped. Can exactly \(2\) heads be obtained?
The parity of heads is preserved because an even number of coins is flipped.
If \(h\) heads are among the flipped coins, the number of heads changes by \(4-2h\), an even number. Parity is preserved. Initially \(15\) is odd; \(2\) is even. Impossible.
Strengthened coin problem.