**Solve**. Place the digits 1, 2, 3, 4 and 5 in the below circles so that the sums across and vertically are the same. Describe the strategy you used to find your solution(s).

**See here**. A complete solution is given below.

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# How to Solve It?

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Mathematics for All

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1 3 5 horizontal

2 3 4 vertically. And vice versa

3 is common and sum is rest two is same both ways.

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Thank you so much for your solution. However, a complete solution is already provided, which includes your one.

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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)

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