[Guest]

There are three friends -- Daniel, David and Dyan. On some day, Daniel gave pens to David and Dyan. After a month David gave as many pens to Daniel and Dyan as they have. After another month Dyan did the same thing. At the end of this transaction each one of them had 24.

Now, the question is how many pens did each originally have?

[Guest]

There are three friends -- Daniel, David and Dyan. On some day, Daniel gave pens to David and Dyan. After a month David gave as many pens to Daniel and Dyan as they have. After another month Dyan did the same thing. At the end of this transaction each one of them had 24.

Now, the question is how many pens did each originally have?

Am I missing something?

We start with X,Y,Z..

X gives Y and Z

Y gives X and Z

Z gives X and Y, in that order

So reverse it,

Pre-final transaction;

Z = 24, X = 12, Y = 12

Pre 2nd Transaction

Z = 12, X = 6, Y = 12

Pre 1st Transaction

Z = 6, X = 6, Y = 6

Or are they giving their own pens away?

Change the names too LOL, I almost did a simple, 24/2/2/2 = 3 (Thought same person was giving away pens)

[Guest]

This is probably more logical..

After Step 3,

X = 24, Y = 24, Z = 24

Before Step 3, (Z doubles x,y)

X = 12, Y = 12

Means Z gave away 24 pens, thus Z had 48

After Step 2

X = 12, Y = 12, Z = 48

Step 2 (Y doubles x and z)

X = 6, Z = 24, Thus Y gave away 30 pens.

After Step 1

X = 6, Y = 42, Z = 24

Before Step 1 (X doubles y,z)

Y = 21, Z = 12. Thus, X gave away 33 Pens.

X = 39, Y = 21, Z = 12

[Guest]

.....

Pre-final transaction;

Z = 24, X = 12, Y = 12

Pre 2nd Transaction

Z = 12, X = 6, Y = 12

Pre 1st Transaction

Z = 6, X = 6, Y = 6

Or are they giving their own pens away?

Change the names too LOL, I almost did a simple, 24/2/2/2 = 3 (Thought same person was giving away pens)

Let initially Daniel has 6, David has 3 and Dyan has 2 pens.

At the end of transaction 1, Daniel will have 1 (bcoz he gives away five), David will have 6 (it is doubled) and Dyan will have 4 pens.

Do you think the change in names make the puzzle harder or easier ? I actually I like these names -- probably at one point I will change my name to Daniel and will have two sons -- David and Dyan

[Guest]

This is probably more logical..

After Step 3,

X = 24, Y = 24, Z = 24

Before Step 3, (Z doubles x,y)

X = 12, Y = 12

Means Z gave away 24 pens, thus Z had 48

After Step 2

X = 12, Y = 12, Z = 48

Step 2 (Y doubles x and z)

X = 6, Z = 24, Thus Y gave away 30 pens.

After Step 1

X = 6, Y = 42, Z = 24

Before Step 1 (X doubles y,z)

Y = 21, Z = 12. Thus, X gave away 33 Pens.

X = 39, Y = 21, Z = 12

Polish has got it. Great.

[Guest]

Polish has got it. Great.

I didn't know which way you were approaching it, as in they both new pens or not so I solved for both.

[akaslickster]

3 pens

[akaslickster]

3 pens then 6?

[Guest]

3 pens then 6?

You mean each of them had 3 pens? I think you need to consider they give each other ... Have a look at my post #4 above, in case you don't understand what the question is.