Problem
Build a number from digit conditions in order
Build a single six-digit number whose six place-value digits satisfy a list of clues, using each of the digits 0, 1, 2, 3, 4 at least once.
Base-ten numbers
Your answer
Watch out The ten-thousands and hundreds digits are 1 less than the ones digit 4, giving 3 — reading it as 1 more wrongly gives 5, which isn't even an allowed digit.
How to solve
Strategy Guess and Check — Each clue pins down one place, so I fix the places I know for certain first (a subproblem per place), then use the 'use every digit' rule to fill the one leftover place, checking the result against all clues.
1STEP 1
Hundred-thousands place
A place value of 200,000 in the hundred-thousands place means that digit is 2.
200,000 = 2 × 100,000
Place value just says how many hundred-thousands there are, so 200,000 is two of them.
4.NBT.A.2Work Backwards2STEP 2
Ones place
The largest of the allowed digits 0,1,2,3,4 is 4, and it goes in the ones place.
ones digit = 4
Among 0,1,2,3,4 the biggest is plainly 4.
4.NBT.A.2Guess And Check3STEP 3
Ten-thousands and hundreds places
These two digits are equal and each is 1 less than the ones digit 4, so both are 3.
4 - 1 = 3
Working backward from the ones digit, '1 less than 4' is 3 for both matching places.
4.NBT.A.2Work Backwards4STEP 4
Thousands place
The thousands digit is given directly as 0.
thousands digit = 0
One clue hands this place to us with no work.
4.NBT.A.2Identify Subproblems5STEP 5
Tens place by 'use every digit'
So far the digits placed are 2, 3, 0, 3, ?, 4. The digits 0, 2, 3, 4 already appear, but 1 has not yet been used, so the only empty place (tens) must be 1.
2 3 0 3 1 4
Every required digit must appear, and 1 is the only one still missing, so it fills the last slot.
4.NBT.A.2Guess And CheckThe tens place, which no clue names on its own, must hold the one required digit that every earlier clue left unused.
Why?
Only the tens place has no clue of its own, and the rule that every required digit must appear forces it to hold whichever required digit is still missing.
Why?
The number is exactly its six place-digits with no place skipped or counted twice, so once five places are pinned exactly one place stays open.
🧱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?
The earlier clues already place 0, 2, 3, and 4, so among the required digits 0,1,2,3,4 only 1 is still unused, and it must go in the open place.
Why?
Each required digit needs a place and each place takes one digit, so the single unused digit and the single open place pair one to one.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Answer
230,314
230,314 is a six-digit number using only 0,1,2,3,4 with all five present; its ones digit 4 is the largest, ten-thousands and hundreds are both 3 (which is 4-1), thousands is 0, and the lead digit 2 gives place value 200,000. Every clue holds.
Takeaway
This only needs Grade 4 place-value sense: pin down each digit from its clue, then fill the last spot with the digit you haven't used yet!
- Hundred-thousands place
- Ones place
- Ten-thousands and hundreds places
- Thousands place
- Tens place by 'use every digit'
Where next?
Another one like thissuggested
Same look, different logicsuggested
Step back and solidifysuggested