AMC 8 · 2001 · #4
Grade 4 number-theoryarithmeticPick an answer.
AMC 8 2001 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Tool #5 (Look for a Pattern) gives the place-value rule: in a multi-digit number, the leftmost place matters most, so to keep the number small we should put the smallest available digit on the left first, then the next smallest, and so on. Tool #6 (Guess and Check) handles the twist — the even-number rule forces the units digit to be 2 or 4, so the greedy left-to-right plan can run into a conflict when it reaches the last two places. When that happens, we swap the units digit and try again.
Greedy left-to-right: place the smallest available digit first, which gives 12349.
Place value says the ten-thousands slot is worth the most, so the smallest digit goes there; then the thousands slot, and so on.
4.NBT.A.2Look For A Pattern12349 ends in an odd digit, so it fails — an even number needs its units digit to be 2 or 4.
A number is even exactly when its units digit is even, and the only even digits available are 2 and 4.
2.OA.C.3Guess And CheckPut the larger even digit 4 in the units place and fill the rest smallest-first, giving 12394.
Sending 4 (rather than 2) to the units place is better because 2 is smaller and helps more in the higher places.
4.NBT.A.2Guess And CheckThe tens digit of 12394 is the second digit from the right: 9.
The tens place is the second digit from the right, which is 9.
4.NBT.A.2Look For A PatternTo shrink a number, push the smallest digits to the leftmost places — but if a rule like "must be even" claims a spot, give that spot the larger acceptable digit so the smaller ones can do more work on the left.