Anh em giúp với !!!

Denote the false weight is x. We divide 14 weights into 4 groups as below:

Note: Case 1_2 means the first case of the second time we balance.

A = {A1, A2, A3, A4}, B = {B1, B2, B3, B4}, C = {C1, C2, C3, C4}, D = {D1, D2}

1st time: We balance

A1, A2, A3, A4 ------------------- B1, B2, B3, B4

Case 1_1: if not equal and we suppose A1, A2, A3, A4 > B1, B2, B3, B4 (1)

2nd time: we balance

A1, A2, B1 ----------------- A3, A4, C1 (2)

Case 1_2: (2) is equal => x = {B2, B3, B4}
From (1) + B1 is true => x is light weight.

3rd time: we balance B2 ---------- B3

Case 1_3: if equal => x = B4
Case 2_3: if not equal + (x is light weight)
=> x is the light weight between B3 and B2.

Case 2_2: (2) is not equal and we suppose that A1, A2, B1 > A3, A4, C1
=> x ={ A1, A2, A3, A4, B1}

3rd time: we balance B1, A3 ---------- A2, C1 (3)

Case 1_3: if equal => x ={A1, A4}.
(1) => x is the heavy weight
(2) A1, A2, B1 > A3, A4, C1 => x = A1

Case 2_3: if not equal => A1 = A4, = C1 and they are all true weights.
=> x ={A2, A3, B1}

a/ If (3) is B1, A3 > A2, C1 (4)
From (2) we also had
A1, A2, B1 > A3, A4, C1 ó B1, A2 > A3, C1 (5)
From (4) + (5) we can conclude that the result of (4) and (5) are the same when A3 and A2 change their place together.
=> B1 is the heavy false weight. => x = B1

b/ If (3) is B1, A3 < A2, C1 (4)
From (2) we also had
A1, A2, B1 > A3, A4, C1 ó B1, A2 > A3, C1 (5)
From (4) + (5) we can conclude that the result of (4) and (5) are not the same when A3 and A2 change their place together.
=> B1 is the true weight. => x ={A2, A3}
From (1) = > x is the heavy false weight + (4) => x =A2

Case 2_1: if equal => x ={C1, C2, C3, C4, D1, D2}

2nd time: we balance C1, C2,C3 --------- A1, A2, A3

Case 1_2: if equal => x ={C4, D1, D2}

3rd time: we balance D1 ---------- C4

Case 1_3: if equal => x = D2
Case 2_3: if not equal => x ={D1, C4}

4th time: we balance D1-----------A1
Case 1_4: if equal => x = C4
Case 2_4: if not equal => x = D1
Case 2_2: if not equal => x ={C1, C2, C3}
we suppose C1, C2 C3 > A1, A2, A3 (2) => x is the heavy weight

3rd time: we balance C1 --------C2
Case 1_3: if equal => x = C3
Case 2_3: if not equal + (2) => x is the heavy weight between C1, C2

 

em chưa có con ..mới năm 2 ĐH àh anh :sun:, bài tap về nhà đó

 

he he ban đầu làm theo cách 3 lần cân nên trừng hợp đầu hơi rối rắm ...đang làm giữa chừng bí quá..mới phát hiện là 4 lần mới ra :kinhdi:..mà đã lỡ làm rồi nên tiếp tục thôi , làm biếng làm lại lắm :sun: