Kc, let me have a look.

When Giselle gives 21 playing cards to Debra,
- Giselle loses 21 cards AND
- Debra gains 21 cards

Agree? The two events above (of losing and gaining) happen at the same time, but what if we describe them differently?

- Giselle loses 21 cards to "nowhere"
- Debra gains 21 cards from "nowhere"

Before Debra gains 21 cards from "nowhere", Debra will have 19 playing cards more than Giselle. This occurs AFTER Giselle loses 21 cards to "nowhere".

Before Giselle loses the 21 cards, Giselle would have 21 more cards than before.

With this, Giselle will have more 2 more playing cards than Debra at first.

So, let's look at it the other way.

If Giselle has 2 more playing cards than Debra at first, and Giselle gives 21 playing cards to Debra,

- Giselle loses 21 cards to nowhere. As a result, Giselle has 19 fewer playing cards than Debra.

- Debra also gains 21 cards from nowhere. As a result, Debra increases the number of playing cards by 21, to bring the total separation to 40 cards.

I give you another story.

I have $5. You have $5. So we have an equal amount of money.

Can you describe to me what happens if I give you my $5? Will you have $5 or $10 more than me?

There is a "double swing" in numbers as you give something to another person. Here, there is a "double swing" of 21 cards when Giselle loses 21 cards and Debra gains 21 cards.

If Giselle loses 21 cards only, not gives 21 cards to Debra, there is only a "single swing" in numbers as Giselle loses 21 cards but Debra goes not gain any cards.

Hi Eric, so your answer to a) is Giselle?

Yup, and for (b) is two cards.

Sorry may i ask why it is not a) Debra and for b) is 19 more?

When Giselle gives 21 playing cards to Debra, Debra ends up having 40 more playing cards than Debra.

You need to be careful with the calculations here, as the question is trickier than a standard scenario.

There are two things happening when Gisele gives 21 playing cards to Debra.

1. Giselle loses 21 playing cards
2. Debra gains 21 playing cards

This is a swing of 42 playing cards. Because of this swing, Debra has 40 more playing cards than Giselle.

So, before this swing of 42 playing cards, Debra must have had 2 fewer playing cards than Giselle at first.

Let’s use numbers to confirm this.

Suppose Debra has 100 playing cards and Giselle has 102 playing cards.

After Giselle gives 21 playing cards,
- Giselle has 102 - 21 = 81 playing cards (Giselle has 21 cards fewer than before, a swing of 21 cards)
- Debra has 100 + 21 = 121 playing cards (Debra has 21 cards more than before, a swing of 21 cards)

Observe that Debra has 40 more playing cards than Giselle at the end (a swing of 42 cards from the original scenario).

If Debra has 19 more playing cards than Giselle, this is what happens.

- Giselle has 100 playing cards at first
- Debra has 119 playing cards at first

At the end,
- Giselle has 100 - 21 = 79 playing cards
- Debra has 119 + 21 = 140 playing cards

This is a difference of 61 cards, or in other words, (19 + 21 + 21) cards, which does not match the story.

There is a double swing of 21 in such a case.

Your answer of 19 would have been correct in this scenario.

Giselle loses 21 playing cards (note that this is not the same as Giselle gives 21 playing cards to Debra), and as a result, Debra has 40 more playing cards than Giselle at the end.

In this case, Giselle loses 21 playing cards, but Debra does not gain any cards at all. This is why Debra has 19 more cards than Giselle at first, because Giselle’s loss of 21 cards widens their gap to 40 cards but Debra does not gain any cards at all (leaving their difference as 40).

In the original story, the gap widens twice - once for Giselle losing 21 cards and once more for Debra gaining cards at the same time.