Number and Place Value Challenge
The Number and Place Value Challenge moves beyond basic reading and ordering of numbers into place-value reasoning puzzles: 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. 11+ papers, especially CEM-style and puzzle-heavy regional tests, favour this 'detective' style of question because it tests understanding of place value rather than just the ability to read a number aloud.
Method
- Write out the place-value columns of the number involved, thousands, hundreds, tens, units, tenths, so you can see exactly which column each clue refers to.
- Work through the clues in the order that narrows the possibilities fastest, usually starting with the clue that fixes the most digits.
- When a clue gives a range, such as 'between 4,000 and 5,000', fix the digits that range confirms before testing individual digits.
- When more than one number could fit, use any remaining clues, such as odd/even or a digit sum, to eliminate options until only one is left.
- Once you have a candidate answer, check it against every clue in the question, not just the last one you used.
- For 'what happens if a digit changes' questions, change only the stated digit and recompute the value of that column, leaving every other column unchanged.
Worked example
I am a four-digit number. My thousands digit is 3. My units digit is double my thousands digit. My hundreds digit is 0. My tens digit is the sum of my thousands and units digits. What number am I?
- The thousands digit is given directly: 3.
- The units digit is double the thousands digit: 2 x 3 = 6.
- The hundreds digit is given directly: 0.
- The tens digit is the sum of the thousands and units digits: 3 + 6 = 9.
- Putting the digits in order, thousands, hundreds, tens, units, gives the number 3,096.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1What is the value of the digit 5 in the number 45,872?Show answer
Answer: 5,000
Q2I am a three-digit number. My hundreds digit is 4. My units digit is 3 more than my hundreds digit. My tens digit is 0. What number am I?Show answer
Answer: 407
Q3Round 68,472 to the nearest thousand.Show answer
Answer: 68,000
Q4What is the smallest four-digit number that can be made using the digits 5, 0, 8 and 2 exactly once, if the number cannot start with 0?Show answer
Answer: 2,058
Q5A number has a 7 in the hundreds place, a 0 in the tens place and a 3 in the units place. What number is it?Show answer
Answer: 703
Q6What is the largest four-digit number that can be made using the digits 9, 1, 6 and 4 exactly once?Show answer
Answer: 9,641
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
I am a four-digit number between 5,000 and 6,000. My units digit is 4. My tens digit is double my units digit. My hundreds digit is half my tens digit. What number am I?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A five-digit number is 5[]732, where [] stands for a single missing digit. If the digit sum of the whole number is 26, what is the missing digit?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the number and place value challenge 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 35 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on number and place value challenge, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.