Question 287851
To understand this question it is helpful to look at smaller cases:
2 coins: pn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0 moves
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3 coins:pnp -> ppn . . . . . . . . . . . . . . . . . . . . . . . 1 move
4 coins:pnpn -> ppnn. . . . . . . . . . . . . . . . . . . . . . 1 move
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5 coins:pnpnp -> ppnnp -> ppnpn -> pppnn . . . 3 moves
6 coins:pnpnpn . . . . . . . . . . . . . . . . . . . . . . . . . . .3 moves
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7 coins: pnpnpnp. . . . . . . . . . . . . . . . . . . . . . . . . . 6 moves
8 coins: pnpnpnpn. . . . . . . . . . . . . . . . . . . . . . . . . 6 moves
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9 coins: pnpnpnpnp. . . . . . . . . . . . . . . . . . . . . . . . .10 moves
10 coins: pnpnpnpnpn. . . . . . . . . . . . . . . . . . . . . . .10 moves
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Notice that the number of moves for each pair after the first will be triangular in nature: 0, 1,3,6,10 and so on.
So, 10 pennies will have 10 moves; ( A )