Example 1  1 or 9 is entered in any of B, D, and I without double arrows in the upper row, but 9 is not entered in B due to K8. Also, when I is 9, H is 8, but 8 is not included in H due to Q6, so D=9. From D9 and C7, G=8. Further, either A or B becomes 6 from G8 and C7, but since 6 does not enter B due to K8, A=6. Next, from F5, either B or E is 4, but even if either is 4, the other is 3, and BorE=3or4. The remaining H=2 and I=1. From the lower row K8, J is either 7 or 9, but when 6 is entered in A, 7 is not entered in J and J=9.  Example 2  Any one of D, F, G, and I in the upper row C3 to D, F, G, and I becomes 2 or 4, but 1 is not followed by any 2 other than G. Therefore, G=2 and I=1. Next, any one of A, B, and E from H7 will be 6 or 8, but both A and B are double arrows, so no matter which one is 8, 9 will not follow. Therefore, E=8 and F=9, which results in D=4 and AorB=5or6. 1 or 9 is entered in any of K, Q, and R without double arrows in the lower row, but 9 is not entered in Q due to H7. Also, from P7, either Q or R is 6 or 8, but Q is not included due to H7, so R=6or8. This gives K=9 and Q=1.  Example 3  In the lower row K4 to L are either 3 or 5. If L is 3, J becomes 2, and if 5, J becomes 6. Next, Q from R7 is either 6 or 8, but if it is 8, it is not followed by 9. Therefore, since Q=6, L=3 and J=2, which results in M=1. In addition, it is located between K4 and Q6, and the double arrow N=5, and the remaining O=8 and P=9. Any one of A to C from the upper row D6 is 5 or 7, but since 5 cannot be entered in B by K4, either A or C is 5. Next, one of G to I from F2 is 1 or 3, but 4 is not included in G to I. In addition, since 4 cannot be entered in either B or E due to the lower row, 4 is entered in either A or C, and AorC=4or5, B=7. Of the remaining G and H without double arrows, 9 cannot be entered in G due to P9, so G=1, P=9, and the remaining E=8, I=3.  Example 4  G to I are 4 or 6 from the upper row F5. First, the double arrow C=3 between 4 and B2. Next, since 6 cannot be entered in G by P6, either H or I becomes 6. For the 6, either A or D is 7, and one of E, G, H, and I is 8. With respect to 8, D=9 without a double arrow among A and D, resulting in A=7. As a result, E is either 1 or 8, and any of G to I is 1, 4, 6, and 8. Any one of M3 to J to L in the lower row is 2 or 4, but neither is included in K due to B2, so JorL=2or4. Then, either Q or R becomes 5 for that 4. Next, either K or O becomes 7 from that 5 and P6, but if K is 7, no matter where the next 8 becomes, 9 will not follow. Therefore, O=7, QorR=5or8, and the remaining K=9 and N=1. Since N becomes 1, E=8, which was not determined in the upper row.  Example 5  From the lower row K6 to J are 5 or 7. From M4, either left or right is 3, and the other is 5. If J is 5, somewhere on the right side of M4 will be 3, and if J is 7, L on the left side will be 3. If L is 3, the only squares left without a double arrow are N and R, so either one of them will be 1 or 9. However, 1 is not included in N due to E2, and 9 is also not included because there is no 8 on the left side. Therefore, J=5. As a result, N is either 7, 8, or 9 because 3 is not included in N due to E2. First, when N is 7, L is 8 and R is 9, which is a contradiction. Also, when N is 8, there is no square in which 7 is placed next, so N=9 and L=8. As a result, in the remaining squares, R=1 without a double arrow, Q=2, O=3, and P=7. From E2 and I4 in the upper row, any of A, B, D, and F is 3. But 3 is not entered in either D or F due to the lower row, and either A or B is 3. From 3 and E2, either G or H without a double arrow becomes 1, but because of Q2, 1 does not enter H and G=1. Next, for I4, A, D, and F cannot enter 5 due to the lower row, so either B or C becomes 5. When B is 5, A=3 and C=6, and when C is 5, A=6 and B=3. Either F or H is 7 for 6, but in both cases D=9 and ForH=7or8.  |
