硬币组合不可唯一确定的最小硬币数

最小为 $N=6$。

例如 0.40 可用 4 枚硬币表示为：1 枚 25 分 + 3 枚 5 分，或 4 枚 10 分。把两种方案都再加 2 枚 10 分即可得到 0.60 且硬币数同为 6。

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Original Explanation

Clearly, $N = 1$ and $N = 2$ don't work, as you can't obtain $0.60 from just one or two coins of these denominations. For$N = 3$, we can see that$2$quarters and$1$ dime work. There are no other ways to obtain the sum besides this.

Now, note that $0.40$ is the smallest denomination that can be written in two different ways using the same amount of coins. Namely, we can use $4$ coins to write $0.40$ as $1$ quarter and $3$ nickels OR $4$ dimes. Therefore, we can just append $2$ dimes to each of these combinations, and we get that $N = 6$ is the smallest value for which this is true.

To verify $0.40$ is the smallest value, we know that the number is at least $0.25$, as otherwise we can't utilize quarters, so test $0.30$ and $0.35$ and see that they don't work.