Palindomania
Level
pending
How many 5-digit even palindromes are there?
(A palindrome is a natural number that is the same when read backwards.)
The answer is 400.
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1 solution
Because this number is a palindrome, we only have to select the first three of the five digits - the remaining two will be equivalent to the first two. The first digit (the same as the last digit) must be even, giving four possibilities. The second and third digit can be any digit, each giving ten possibilities. The last two digits are dependent on the first two. The total number of possibilities is then 4 ∗ 1 0 ∗ 1 0 = 4 0 0 .