Discussion

Explanation:

The chit picked by Gabra in round 3 = 25443 – (9867 + 6897) = 8679

The chit picked by Kabra in round 1 = 25371– (9876+ 6798) = 8697

Now, the various equations that can be formed are:

a + b = 26469 – 7986 = 18,483

This is only possible when the two numbers are of the form 9pqr and 8xyz.

Since last digit of r + z is 3, this is possible when one of r or z is 6 and the other is 7.
Carry over of r + z will be 1.

Now, last digit of 1 + q + y = 8, hence last digit of q + y is 7.
This is possible when one of q or y is 8 and the other is 9.
Carry over of 1 + q + y = 1

Now, last digit of 1 + p + x = 4, hence last digit of q + y is 3.
This is possible when one of p or x is 6 and the other is 7.

∴ a + b can be (9786 + 8697) or (9687 + 8796) in any order.

Since, Kabra picked 8697 in 1st round, Abra cannot pick 8697.

Hence a or b can be 9687 or 8796.

Case 1: a = 9687
⇒ f = 51093 – (9687 + 9768 + 6987 + 9867 + 8697) = 6087
This is not possible since the digits should be either 6, 7, 8 or 9.

Case 2: a = 8796
⇒ f = 51093 – (8796 + 9768 + 6987 + 9867 + 8697) = 6978

∴ a = 8796, b = 9687 and f = 6978

Now, 149103 = 26469 + 25524 + (6987 + e + 7968) + 23643 + 25443 + 25371
⇒ e = 7698

Also, c = 46935 – (7986 + e + 7689 + 6897 + 9876)
∴ c = 6789

Also, d = 25524 – (9768 + c)
∴ d = 8967

This final table is as follows:

​​​​​​​

Hence, Dabra picked 6978 in round 1.

Hence, 6978.

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