Sensim Math · Depth 한국어

4-1 · Large Numbers

Build a number from digit conditions in order

4.NBT.A.2 · adapt · grade 4

Archetype: Pin Down a Number from Digit and Range Conditions · step in a 9-type progression

▶ Practice — 10 problems

Find the number that satisfies all of the following conditions.

Show solution

Understand

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.

Givens
  • The number has six digits (hundred-thousands down to ones).
  • Each of the digits 0, 1, 2, 3, 4 is used.
  • The largest digit sits in the ones place.
  • The ten-thousands digit equals the hundreds digit, and it is 1 less than the ones digit.
  • The thousands digit is 0.
  • The hundred-thousands digit has place value 200,000.
Unknowns
  • The six-digit number that satisfies every condition
Constraints
  • Only the digits 0, 1, 2, 3, 4 may appear, and all five must show up at least once.
  • A six-digit number cannot start with 0.

Plan

#6 Guess and Check · also uses: #7 Identify Subproblems#11 Work Backwards

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.

Execute

#11 Work Backwards 4.NBT.A.2
A place value of 200,000 in the hundred-thousands place means that digit is 2.
200,000=2×100,000200{,}000 = 2 \times 100{,}000
Place value just says how many hundred-thousands there are, so 200,000 is two of them.
#6 Guess and Check 4.NBT.A.2
The largest of the allowed digits 0,1,2,3,4 is 4, and it goes in the ones place.
ones digit=4\text{ones digit} = 4
Among 0,1,2,3,4 the biggest is plainly 4.
#11 Work Backwards 4.NBT.A.2
These two digits are equal and each is 1 less than the ones digit 4, so both are 3.
4−1=34 - 1 = 3
Working backward from the ones digit, '1 less than 4' is 3 for both matching places.
#7 Identify Subproblems 4.NBT.A.2
The thousands digit is given directly as 0.
thousands digit=0\text{thousands digit} = 0
One clue hands this place to us with no work.
#6 Guess and Check 4.NBT.A.2
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  42\;3\;0\;3\;\boxed{1}\;4
Every required digit must appear, and 1 is the only one still missing, so it fills the last slot.
Answer: 230,314

Review

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.

Make a systematic list (tool 2): write the place names in a row, fill each from its clue, and the single blank that remains forces the missing digit 1.

Standards · min grade 4

  • 4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Reading each place value and assembling the six-digit number from the digit clues.
💡 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!