Here is a mystery number's first clue: "I have three tenths and no hundredths."

Say what you think the number could be. Could there be more than one answer from just this one clue, or does it already pin the number down?

Three clues, and between them they narrow one mystery decimal down to a single answer. Watch the place-value mat after each clue and keep a list of which numbers are still possible.

1. Clue 1 narrows a lot. Three tenths and four hundredths, with the thousandths still hidden. That leaves ten possibles, 0.340 up to 0.349.
2. Clue 2 narrows nothing, and that is the thing to notice. Between 0.3 and 0.35. Every one of our ten is already inside those fences, so none are ruled out. It is still a true clue, and it would have ruled out 0.36 or 0.4 if they had been on the list. A clue can be true and still do no work.
3. Clue 3 finishes it. Multiplying by 100 gives a whole number. 0.340 × 100 = 34, but 0.341 × 100 = 34.1, so every candidate with a thousandths digit above zero is out.

One number survives all three: 0.34.

Today we work through one full mystery number together, clue by clue. Here are the four clues in the order we will meet them:

Clue 1: I am a decimal with two decimal places. My tenths digit is 4.
Clue 2: My hundredths digit is bigger than 5.
Clue 3: When you round me to the nearest tenth, I round up to 0.5.
Clue 4: My hundredths digit is odd.

After each clue we will build one surviving candidate at a time on the place-value mat to check it still fits, and cross off any that a new clue rules out on the board. Predict, before clue 4, how many numbers are still standing.

Today you crack a five-clue paper puzzle to find one mystery three-decimal-place number. Solving each clue narrows the list until the last clue reveals the single answer.

The five clues, in order:

Clue 1: I have three decimal places and my tenths digit is 6.
Clue 2: My hundredths digit is zero.
Clue 3: I am bigger than 0.6 but smaller than 0.61.
Clue 4: My thousandths digit is a multiple of 4 (and not zero).
Clue 5: My thousandths digit is smaller than 6.

Work each clue in turn on your paper, crossing off numbers as you go. What single number is left when clue 5 is done?