One candle suffices. Take one candle from the box labeled "white and red." Say that it's white. You know that this must be the white box, therefore the box labeled "red" must contain mixed and the box labeled "white" must actually be the red candles.

In the four-box case, the answer is three.

Number the boxes from 1 to 4, so that Box 1 is labeled P&N, Box 2 is labeled N&D, Box 3 is labeled D&Q, Box 4 is labeled Q

First, request Box 3. If the coin from Box 3 is a dime or quarter, request Box 2, and whatever comes out, you will have enough information to know which two boxes to choose. Namely:

If ?NQ?, meaning a nickel (or penny) from Box 2 and a quarter from Box 2, then choose boxes 1 & 4. If ?QD? then choose boxes 1 & 2. In all other cases (?ND?, ?DD?, ?DQ?, ?QQ?) choose boxes 1 & 3.

If the coin from Box 3 is a nickel (or penny), request Box 1 next. If the coin from Box 1 is also a nickel, choose boxes 1 & 4. If the coin from Box 1 is a dime, request Box 4; if it's a quarter, request Box 2. Then choose as follows:

If D?NN then choose boxes 1 & 2. If D?ND then choose boxes 1 & 4. If D?NQ then choose boxes 1 & 4

If QNN? then choose boxes 1 & 3. If QDN? then choose boxes 1 & 2. If QQN? then choose boxes 1 & 2.