Number and Place Value Challenge Set 2
Number and Place Value Challenge Set 2 continues the 'detective' style of question found in the first Challenge set: working out a missing digit, finding a number that fits several place-value clues at once, and reasoning about what happens to a number's value when a digit changes. CEM-style and puzzle-heavy regional 11+ papers favour this style because it tests understanding of place value rather than just the ability to read a number aloud.
Before you start
Make sure you're comfortable with these topics first:
Method
- Set out the place-value columns of the number involved so you can see exactly which column each clue is describing.
- Work through the clues in the order that pins down the most digits first, rather than in the order they happen to be written.
- Where a clue gives a range, for example 'between 6,000 and 7,000', use it to fix digits before testing individual values.
- If more than one number still fits, use any remaining clue, such as odd or even, a digit sum, or a comparison between digits, to eliminate the rest.
- Once a candidate number is found, check it against every clue given, not only the one used most recently.
- For 'change one digit' questions, alter only the named digit and recompute the value of that column, leaving the rest of the number unchanged.
Worked example
I am a four-digit number. My thousands digit is 6. My units digit is half my thousands digit. My hundreds digit is triple my units digit. My tens digit is my hundreds digit minus 5. What number am I?
- The thousands digit is given directly: 6.
- The units digit is half the thousands digit: 6 / 2 = 3.
- The hundreds digit is triple the units digit: 3 x 3 = 9.
- The tens digit is the hundreds digit minus 5: 9 - 5 = 4.
- Putting the digits in order, thousands, hundreds, tens, units, gives the number 6,943.
Practice questions
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Q1What is the value of the digit 6 in the number 67,204?Show answer
Answer: 60,000
Q2I am a three-digit number. My hundreds digit is 5. My units digit is 2 more than my hundreds digit. My tens digit is 1. What number am I?Show answer
Answer: 517
Q3Round 74,528 to the nearest thousand.Show answer
Answer: 75,000
Q4What is the smallest four-digit number that can be made using the digits 7, 0, 3 and 9 exactly once, if the number cannot start with 0?Show answer
Answer: 3,079
Q5A number has a 4 in the thousands place, a 0 in the hundreds place, an 8 in the tens place, and a 6 in the units place. What number is it?Show answer
Answer: 4,086
Q6What is the largest four-digit number that can be made using the digits 2, 8, 5 and 1 exactly once?Show answer
Answer: 8,521
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
I am a four-digit number between 3,000 and 4,000. My units digit is 4. My hundreds digit is double my units digit. My tens digit is half my hundreds digit. What number am I?
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A five-digit number is 6[]481, where [] stands for a single missing digit. If the digit sum of the whole number is 28, what is the missing digit?
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A four-digit number has a digit sum of 21. Its thousands digit is 5, its hundreds digit is 3 more than its thousands digit, and its units digit is half its hundreds digit. Find its tens digit, and hence find the number.
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Free printable worksheet
Want more practice on paper? Download the number and place value challenge set 2 worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 36 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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