I won't be able to draw model here as the chat box does not allow me to draw models.

Andy is able to give either 1/3 or 1/2 of his share to Ben. So, Andy's number of stamps must be divisible by both 3 and 2.

What number is divisible by 3 and 2? Maybe...6?

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Let's say Andy starts out with 6 units.
Andy gives 1/3 of his share, or simply 2 units, to Ben.

So, in the first model, Andy has 4 units.

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If Andy were to give 1/2 of his share to Ben, he is essentially giving away 3 units to Ben, so that Andy only has 3 units left.

So in the second model, Andy has 3 units, which is basically 1 unit fewer than in the first model. Ben will also gain this 1 unit.

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In the process from the first model to the second model,

- Andy loses 1 unit
- Ben also gains 1 unit
- This means that the gap between Andy and Ben widens by 2 units

The 2 units of widening is the reason why Ben's "advantage" increases from 20 stamps to 50 stamps, or basically an extra 30 stamps.

2 units = 30 stamps
1 unit = 15 stamps
6 units = 90 stamps

So, Andy has 90 stamps.

You can easily check from here that Ben will have 50 stamps at first, and you can verify your answer accordingly.

Thank you very much.

Ans: 90

½ , ⅓
LCM(2,3) → 6
3 - 2 = 1
2×1 = 2
2u = 50-20= 30
6u = 90 (Ans)