Question

A game board was set with multiple decks of cards arranged in such a way that sum total of the cards on each side was equal (1+2+3+4=10). However, a new card was added on one side (blue card) and the cards were rearranged to maintain the rule, namely, that the sum total equals 10. How many cards can be added (starting from original position as shown on the left) before the game ends and no more cards can be added? Assume that every position must have at least one card and the sum total rule of 10 must be followed.

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

The Correct Option is B

The initial setup of the game requires the sum of cards on each side to be 10. This means there are fixed card values on either side (1+2+3+4) that total to 10.
When a new card (blue card) is added to one side, the cards are rearranged to maintain the sum of 10 on both sides. The objective is to determine how many such additional cards can be added while following the rules. Here's a step-by-step breakdown:

• The starting configuration of the card values is 1, 2, 3, 4. The sum is 10, fulfilling the initial condition.
• When a new card is added, say `x`, it's placed on one side, requiring a simultaneous rearrangement to maintain the sum of 10 on either side.
• Each position must have at least one card, and differences in value must be balanced by adjusting configurations.
• We must calculate the maximal additional card count before it's impossible to balance to 10.

Consider permutations. Start by adding 1 more card (`x = 5`), the values rearrange from (1, 2, 3, 4, 5):

• Step 1: 4 cards + 5 = 9 (4 values only), requiring rearranged configs.
• Add: (5) to side, remove from initial group to maintain ≤10.
• Cards (1, 4, 5), allows only values shifted elsewhere.

Step	Card Values	Sum
Initial	1, 2, 3, 4	10
Add 1	Cards re-balanced	10
2nd add	Re-arrange final values	10
3rd add	Continue till impossible	10

The ongoing pattern of adjustments and configurations shows a max flow addition consistent with maintaining rules of all sides ≤ 10. Calculation checks numbers are 6 cards extra on every new controlled value.
The correct solution with above reasoning is: 6 cards can be added maximizing balance.