Problem
Find a number from digit clues
A four-digit number between 4000-5000. Hundreds digit 6, digits sum to 20, tens = ones. What is it?
Base-ten numbers
Your answer
Watch out 20 is the sum of all four digits
How to solve
1STEP 1
Fix the thousands & hundreds
A number in the 4000s starts with 4. The clue fixes hundreds as 6. So far it is 4 6 _ _.
"Between 4000-5000" means 4000-4999. The leading digit says how many thousands, so the 4000s have thousands digit 4.
4.NBT.A.2Four Digit Numbers2STEP 2
Find the two equal digits
The sum is 20, but 4+6 is already 10. The last two add to 10, and being equal they are each 5.
4 + 6 + d + d = 20 → d = 5
Call the last two digits d; tens=ones so both are d. Then d+d=10 → d=5.
Guess And Check4.NBT.A.2The 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.
Answer
4655
4000 + 600 + 50 + 5 = 4655
Check — 4655 is in 4000-5000, hundreds 6, 4+6+5+5=20, tens and ones both 5.
Takeaway
Take clues one at a time — each fixes a digit. Equal digits summing to 10 are both 5!
- Thousands & hundreds → 4 6
- Sum 20 → last two are 5 each
- Assemble → 4655
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