Here is our first clue: "I have seven hundredths and three tenths."

What could my mystery number be? This is a think-first moment, so just work it out in your head for now. Lots of numbers still fit, because we only know two of the columns so far, so it is fine if you cannot name just one number yet.

Two clues about mystery numbers are shown on the place-value mat. Notice which columns each clue fills in, and notice that the two clues work in very different ways.

Today we work through one full mystery puzzle together, one clue at a time, on the place-value mat. Because this puzzle goes to three decimal places, we add a fourth column, the thousandths, to the right of the hundredths. Each clue tells us about one more column, and rules out every number that does not fit it. Read each clue, build what we know so far, and say what is still open.

• Clue A: I am bigger than 0.5 and smaller than 0.6.
• Clue B: My hundredths digit is 2.
• Clue C: My thousandths digit is 5.

Clue A gives us the tenths column. Clue B and Clue C then fill the smaller columns, one at a time, until the whole number is built. Read it aloud in words to check it sounds right.

Now solve a five-clue mystery. In your maths copy, sketch the place-value mat and, after every clue, write the shrinking list of candidates (what is still open). Cross off anything that no longer fits. We will check the final number together on the interactive.

First, here is one full worked example so you can see the method end to end. The mystery number is built clue by clue:

• Clue A: I am a decimal with three decimal places. Still open: 0.???.
• Clue B: I am bigger than 0.3 and smaller than 0.4. Tenths fixed at 3. List shrinks to 0.3??.
• Clue C: My hundredths digit is odd. Candidates left: 0.31?, 0.33?, 0.35?, 0.37?, 0.39?.
• Clue D: My hundredths digit is 7. List shrinks to 0.37?.
• Clue E: My thousandths digit is 5. Only 0.375 remains.

Your turn. Work these five clues the same way, writing the shrinking list after each one:

• Clue 1: I am a decimal with three decimal places.
• Clue 2: I am bigger than 0.6 and smaller than 0.7.
• Clue 3: My hundredths digit is greater than 2 and less than 6.
• Clue 4: My hundredths digit is 4.
• Clue 5: My thousandths digit is double my hundredths digit.

When you have the mystery number, answer in your maths journal in one sentence: which clue was the cleverest, and why?