the numbers 0 through 9 written in sequence or any portion of that sequence
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Oh, dude, consecutive identical digits are just fancy words for when you have the same number back-to-back. Like when you see 22 or 777 in a row. It's not rocket science, just a fun little pattern that shows up in numbers.
Find the greatest product of five consecutive digits in the 1000-digit number.7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450
They all have consecutive digits within them.
If a number An consisting of n consecutive digits in ascending order is subtracted from the number An' obtained by reversing the digits of An, then the difference is always a constant. This constant is termed as the 'Unique number' Un as reported by me earlier in. For example, a 3-digit number 345 if subtracted from its reverse 543, yields a difference of 198. Thus U3 = 198. Another 3-digit number, say, 678 if subtracted from its reverse 876 will also yield the same difference, that is, 198. Thus for any number consisting of 3 consecutive digits, the Unique number U3 is always 198. Similarly for a number consisting of 4 consecutive digits, the Unique number U4 = 3087.
There is no pair of consecutive even integers whose sum is 264 - as their average is divisible by 4, that must mean that the sum of the unit digits of each of the pair of numbers could never be a multiple of 4 - which 264 is.