Write a number backwards and add it to the original. Do it again with the answer, and keep going until you get a palindrome, a number that reads the same both ways: 57 + 75 = 132, then 132 + 231 = 363. Most numbers below 10,000 get there in a step or two, but 89 takes 24. Nobody has ever got 196 there, though computers have taken it to a billion digits.
Run a number
196 + 691 = 887, and 887 isn't a palindrome, so round it goes again. Type a number to watch it run.
How far can 196 go?
Your browser keeps reversing and adding, one line per step. Digits that match the digit in their mirror position print in full ink and the rest print faint, so a palindrome would come out as one solid line.
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It runs until you pause it. Romain Dolbeau's program got to a billion digits in 2015 and found no palindrome.
Every number below 10,000
How many steps each one takes to reach a palindrome. Tap a bar to run a number from it.
Steps to a palindrome
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Most need one or two steps, and 89 and 98 need 24. Then a gap, and the question mark: 246 numbers with no palindrome after 1,000 steps.
Why the carries spoil it
Line a number up over its reverse and each column adds the same two digits as its mirror column. In 89 + 98, the ones column is 9 + 8 and the tens column is 8 + 9. If nothing carried, the answer would always be a palindrome, like 123 + 321 = 444.
Carries break the mirror. 9 + 8 = 17 writes the 7 and carries the 1 into the tens column, but nothing carries into the ones column, its mirror. So the tens column makes 18, and 89 + 98 = 187. The longer the number, the more columns there are to carry, and the harder it gets for the carries to come out symmetric.
A number that never reaches a palindrome is called a Lychrel number, and in base 10 nobody has proved that a single one exists. 196 is the smallest candidate. John Walker set a computer on it in August 1987; it stopped at a built-in limit of a million digits in May 1990, after 2,415,836 steps. Romain Dolbeau's program passed a billion steps in 2011 and reached a billion digits in February 2015. No palindrome turned up, but that proves nothing either way: one could still be further on. In base 2 the question is settled: 10110, which is 22, provably never gets there.
Below 1,000 there are 13 numbers that haven't got there: 196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, 978 and 986. Most are 196's path in disguise. 887 is its first step, and nine others land on its path after one step, like 295 + 592 = 887. Only 879 and 978 go somewhere else: both make 1857, which 196's path jumps over on its way from 1675 to 7436.