Track / Stage 4 / 204 of 340 #464 of 2000

Problem 464

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

12. (10 points) Fill in each cell with a number from $1 \sim 6$ , such that the numbers in each row and each column are unique. The numbers on the right indicate the sum of the three-digit number, the two-digit number, and the single-digit number formed by the first three numbers, the middle two numbers, and the last number, respectively, separated by thick lines. What is the five-digit number $\overline{\mathrm{ABCDE}}=$ $\qquad$

Your answer

Official solution

【Answer】Solution: Based on the unit digit and the unit digit that can form the result: If the unit digit of the result is 5, then the unit digits of these 3 numbers must be the combination of $4,5,6$ .

Unique method, elimination method: Only one number can be filled in.
First digit analysis method: The result of the sixth row is 669, so the hundred's digit must be 6.
As shown in the figure:
Therefore, the answer is: 41244

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.