Puzzle of the Week #217 - Identical Twins

Phyllis and Dilys are identical twins. They are each independently given the same 4-digit number.

Phyllis takes the number and converts it from decimal (base 10) to base 4, and writes down the 6-digit result.

Dilys simply writes the first and last digits of the number followed by the number in its entirety.

They are astonished to find that they have both written down the same 6-digit number!

What was the original number?


In other words, which number ABCD, when converted from decimal to base 4 becomes ADABCD?