How to Solve It?

Solve. (a) Using each of the digits 0, 1, 2, 3, 4, 5, 6 and 7 once, fill in the spaces below so that the difference is 8 in the hundreds place, 8 in the tens place, and 9 in the ones place.

(b) Is there more than one solution to this problem? How?

(c) Is there more than one solution in which the digit in the thousands place of the difference is 0?

See here.

3 comments

  1. If x1,x2,x3,x4 &x5 are 5 numbers ;
    If Any xi comes in center i=1,2,3,4,5;
    Then sum of two is sum of remaining two excluding xi;
    If xi=1 remainings are 2,3,4 &5 :- 2+1+5( let it be Horizontal)=3+1+4(let it be vertical);
    3+1+4 ( let it be Horizontal)=2+1+5(let it be vertical);

    If xi=2 remainings are 1,3,4 & 5:- Solution not possible;
    If xi=3 remainings are 1,2,4 &5 :- 1+3+5(H)=2+3+4(V);
    2+3+4(H)=1+3+5(V);
    If xi=4 remainings are 1,2,3 & 5:- Solution not possible;
    If xi=5 remainings are 1,2,3,4 – (1+5+4)(H)=(2+5+3)(V);
    (2+5+3)(H)=(1+5+4)

    Liked by 1 person

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