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You have in your pocket a set of U.S. coins.1
Using these coins you can count out a face-value total2 of exactly $96¢$, $97¢$, $98¢$, or $99¢$, using exactly the minimum number of coins possible for each of those respective amounts.
Moreover, you have only the minimum number of coins in your pocket for which the above is possible.

  • How many coins are in your pocket?
  • What denominations are they?
  • With what minimal set of these coins can you count out exactly 96¢?
  • With what minimal set of these coins can you count out exactly 97¢?
  • With what minimal set of these coins can you count out exactly 98¢?
  • With what minimal set of these coins can you count out exactly 99¢?

1 Limited to real, circulated currency coins issued by the United States Mint.
2 Mis-struck, old, or otherwise rare coins may be more valuable than the coin's stated face value;
    for this puzzle we ignore this, and only use the stated face values of the coins when determining "value".

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  • 4
    $\begingroup$ For those not from the U.S. (such as myself), what are the possible values of U.S. coins? $\endgroup$ – Volatility Dec 21 '16 at 11:28
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    $\begingroup$ here's a list $\endgroup$ – Beastly Gerbil Dec 21 '16 at 11:38
  • $\begingroup$ You also have 1$ coin (not that it is of any help here). $\endgroup$ – Matsmath Dec 21 '16 at 11:39
  • $\begingroup$ Amazing. 5 people so far have found this puzzle good enough to answer but not good enough to ^vote while at it. $\endgroup$ – humn Dec 21 '16 at 12:12
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    $\begingroup$ @humn Why should people upvote just because they leave an answer? $\endgroup$ – Bungicasse Dec 21 '16 at 12:13
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If we interpret

"circulated currency" as "in circulation at some point in time, not necessarily now",

then we can have

6 coins: 50c, 25c, 20c, 3c, 2c, and a 1c.

Using these, you can get the appropriate values by

counting the 50c, 25c, and 20c pieces, and then
- 1c for 96c
- 2c for 97c
- 3c for 98c
- 3c and 1c for 99c

which adheres to the rule that each of the values can be made by the minimum number of coins.

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  • $\begingroup$ Oh man that list of U.S. coins from @Beastly Gerbil threw me off. Good find tho. $\endgroup$ – Bungicasse Dec 21 '16 at 12:16
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From the set of coins

{4x 1c, 2x 10c, 1x 25c, 1x 50c}

you can get

(2x10+25+50)c=95c

So adding up the required number of 1c coin(s) will give you 96c, 97c, 98c, and 99c. These are optimal.

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  • $\begingroup$ Not optimal; you can do better than this. $\endgroup$ – Rubio Dec 21 '16 at 11:39
  • $\begingroup$ So it is a trick question then :(. I am deeply disappointed. $\endgroup$ – Matsmath Dec 21 '16 at 11:40
  • $\begingroup$ There is more to it than the glaringly obvious, or it wouldn't be worth asking. $\endgroup$ – Rubio Dec 21 '16 at 11:42
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    $\begingroup$ @humn just cause you answer a puzzle, doesn't mean you have to upvote it. It might be a rubbish puzzle! (Not saying this one is) $\endgroup$ – Beastly Gerbil Dec 21 '16 at 12:02
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    $\begingroup$ @humn, fair point. I firmly believe in the principle, that users vote for whatever reasons. I might vote up a post on sunny days, otherwise I might just leave it alone. $\endgroup$ – Matsmath Dec 21 '16 at 14:31
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More of a lateral-thinking approach:

enter image description here Where the minus is created from any coin put on its edge and number of pennies is 1, 2, 3 or 4.

So we use

6 coins: 1 dollar, 4x 1 cent and 1 any coin

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  • $\begingroup$ lateral-thinking is quite deliberately absent here. Sorry. $\endgroup$ – Rubio Dec 21 '16 at 12:14

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