Problem
Find a number from digit clues
Find the four-digit number that is between 4000 and 5000, has hundreds digit 6, has digits adding to 20, and has equal tens and ones digits.
Base-ten numbers
Your answer
Watch out The total 20 counts all four digits, including the 4 and 6 already fixed, not only the two unknown digits.
How to solve
Strategy Guess and Check — Each clue pins down one place value, so I work through the conditions in order to nail the thousands and hundreds digits, then solve a small equation for the matching tens and ones digits.
1STEP 1
Fix the thousands and hundreds digits
Between 4000 and 5000 forces the thousands digit to 4, and the clue gives hundreds 6, so the number is 4 6 _ _.
4000 ＜ n ＜ 5000 → thousands = 4, hundreds = 6
A number in the 4000s must start with 4, and a stated hundreds digit is just read straight off.
4.NBT.A.2Identify Subproblems2STEP 2
Use the digit sum to find the equal digits
Digits total 20 and 4 + 6 = 10, so the last two must add to 10; being equal, each is 5.
4 + 6 + d + d = 20 → 2d = 10 → d = 5
Two equal digits that total 10 can only both be 5.
4.NBT.A.2Guess And CheckThe tens digit and the ones digit are each 5.
Why?
The tens and ones digits have to add up to 10.
Why?
All four digits add to 20, and the thousands and hundreds digits already make 4 + 6 = 10, so the last two digits must make the remaining 10.
Why?
The total 20 is just the four digit amounts joined with nothing missing and nothing counted twice, so the parts have to add back to it.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Taking the known 10 back out of the total 20 to see what is left over is subtraction undoing addition.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
Two equal digits that add to 10 must each be 5.
Why?
Adding a digit to an equal copy of itself is that digit counted two times, so the sum is double the digit.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
If double the digit is 10, then splitting 10 back into two equal parts gives 5, because dividing undoes doubling.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
3STEP 3
Assemble the number
Thousands 4, hundreds 6, tens 5, ones 5 gives 4655.
4655
Placing each found digit in its place builds the answer.
4.NBT.A.2Identify SubproblemsAnswer
4655
Check 4655: it is between 4000 and 5000, the hundreds digit is 6, the digits 4+6+5+5 = 20, and the tens and ones digits are both 5. All four conditions hold.
Takeaway
Take the clues one at a time: each one fixes a digit, and two equal digits summing to 10 must both be 5!
- Fix the thousands and hundreds digits
- Use the digit sum to find the equal digits
- Assemble the number
Where next?
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