sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. she stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. what is the sum of the numbers on the middle three cards?

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QWwhite QWwhite · Answer 1 · 2022-11-03T12:10:04-04:00

The sum of the middle 3 numbers according to the positions Sally arranged the blue and red cards in is 12.

It is given that Sally has Red cards 1 to 5 and Blue cards 3 to 6

Let the Red cards be

Similarly, Let the Blue cards be

Since they are positioned alternatively, the position of the cards will be

R B R B R B R B R

It is given that red cards should be placed such that it divides evenly into the neighboring blue cards.

This implies that the red cards should be a factor of the blue cards next to them.

The blue card B5 has only 2 factors, i.e 1 and 5 among the red cards.

Hence, it will be placed between R1 and R5, with R5 at the very end.

Hence we get

R5 B5 R1 B R B R B R

The other prime number among blue is B3 which would be placed between R1 and R3 since those are its factors. Hence we get

R5 B5 R1 B3 R3 B R B R

Now we will place B6 next to R3. Then we will place R4 and at last B4 and R4 to get

R5 B5 R1 B3 R3 B6 R2 B4 R4

The three middle cards are B3, R3, and B6.

Therefore, the sum of the numbers on these cards will be

3 + 3 + 6

= 12

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