This problem, with a slight rewording by me, comes from 'Mathematical Excursions', by Helen Abbot Merrill (pg. 59). I hope I haven't mangled it too much for it to make sense.
The first digit of a given integer (n) is 2. If that first digit is
removed from the front of the number and appended to the rear of the
number, to create a new number, then the new number is exactly half the original number.
What was the original number n?
SPOILER
This problem, with a slight rewording by me, comes from 'Mathematical Excursions', by Helen Abbot Merrill (pg. 59). I hope I haven't mangled
it too much for it to make sense.
The first digit of a given integer (n) is 2. If that first digit is
removed from the front of the number and appended to the rear of the
number, to create a new number, then the new number is exactly half the original number.
What was the original number n?
On Sat, 9 May 2026 16:20:29 -0000 (UTC), David Entwistle wrote:
This problem, with a slight rewording by me, comes from 'Mathematical Excursions', by Helen Abbot Merrill (pg. 59). I hope I haven't mangled
it too much for it to make sense.
The first digit of a given integer (n) is 2. If that first digit is
removed from the front of the number and appended to the rear of the number, to create a new number, then the new number is exactly half the original number.
What was the original number n?
I arrived at the correct answer by plodding through the digits one-by-one. Having read Ilan's much more sophisticated answer, I followed that method, successfully. Here's another similar, but somewhat easier, problem to practice on.
The first digit of a number is 4. If it is shifted to the end, the new number is one fourth the original number.
What was the original number?
Mathematical Excursions is a nice book full of interesting problems and insights.
I arrived at the correct answer by plodding through the digits one-by-one. >Having read Ilan's much more sophisticated answer, I followed that method, >successfully. Here's another similar, but somewhat easier, problem to >practice on.
The first digit of a number is 4. If it is shifted to the end, the new >number is one fourth the original number.
What was the original number?
Mathematical Excursions is a nice book full of interesting problems and >insights.
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