there are two 1's,two 2's,and two 3's.There is one digit between the two 1's, there are two digits between the two 2's, and there are three digits between the two 3's. Holding number cards,can you duplicate this sequence of numbers?

Have you tried labeling six index cards with 1, 2 and 3 and work with arranging (and rearranging) them?

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Yes, it is possible to duplicate this sequence of numbers using number cards. Here's how:

1. Start by laying out the number cards in a row: 1, 1, 2, 2, 3, 3.
2. Place one of the number 1 cards on your left hand and the other number 1 card on your right hand. This creates one digit between the two 1's.
3. Put the number 2 cards in between your hands. This creates two digits between the two 2's.
4. Finally, place the number 3 cards between your hands. This creates three digits between the two 3's.

So now, by holding the number cards in your hands as described, you have successfully duplicated the given sequence of numbers.