7cea837eb18568ff3ee698bf06d6040348e6003599796706a2


Let's begin by noting that xx is given to be a natural number between 1 and 5. (That is, x∈{1,2,3,4,5}x\in\{1,2,3,4,5\}.) When a puzzle restricts a missing number to such a small set, it often means that the relation isn’t an elaborate arithmetic formula producing huge numbers but is hidden in a “nice‐to‐check” property. One clever idea is to “look at the digits” of the numbers.

Let’s examine the first matrix:

(131617100)\begin{pmatrix} 13 & 16\\[1mm] 17 & 100 \end{pmatrix}

A useful approach is to sum the individual digits of each entry. (For example, for 13, 1+3=41+3=4.)

  • Top row:

    • 1313: digit sum is 1+3=41+3=4.
    • 1616: digit sum is 1+6=71+6=7.

    Thus the top row “digit‐sum” is 4+7=114+7=11.

  • Bottom row:

    • 1717: digit sum is 1+7=81+7=8.
    • 100100: digit sum is 1+0+0=11+0+0=1.

    Thus the bottom row “digit‐sum” is 8+1=98+1=9.

The difference between the top row and bottom row digit sums in this matrix is

11−9=2.11 - 9 = 2.

Now, let’s see if the same idea can be applied to the second matrix:

(364548x)\begin{pmatrix} 36 & 45\\[1mm] 48 & x \end{pmatrix}

Again, compute the digit sums:

  • Top row:

    • 3636: digit sum is 3+6=93+6=9.
    • 4545: digit sum is 4+5=94+5=9.

    So the top row digit sum is 9+9=189+9=18.

  • Bottom row:

    • 4848: digit sum is 4+8=124+8=12.
    • xx: Since xx is a one‐digit number (from 1 to 5), its digit sum is just xx itself.

    Thus the bottom row digit sum is 12+x12+x.

If we require that the “digit sum difference” (top row minus bottom row) is the same as in the first matrix—that is, equal to 2—then we must have

18−(12+x)=2.18 - (12+x) = 2.

Let’s solve this equation step by step:

  1. Expand the parentheses: 18−12−x=2.18 - 12 - x = 2.
  2. Simplify 18−1218-12: 6−x=2.6 - x = 2.
  3. Solve for xx by subtracting 2 from 6: 6−2=x⟹x=4.6 - 2 = x \quad \Longrightarrow \quad x=4.

The solution x=4x=4 is indeed within the allowed set {1,2,3,4,5}\{1,2,3,4,5\}.

Thus, by noticing that the difference between the top‐row and bottom‐row digit sums is 2 in the first matrix—and requiring that the second matrix follow the same pattern—we deduce that the missing number is 4


I hope this explanation clarifies the reasoning!




o3식 풀이: 윗 행의 자릿수 합+아랫행의 자릿수 합의 마이너스가 2가 되어야 함 (1+3+1+6)-(1+7+1+0+0)=2


지금까지 다른 모델들은 297 같은 보기에 없는 답을 내거나 아니면 대충 찍던데, 푸는거 보는건 o3가 처음임 ㄷㄷ



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