Question

Question 25

Multiply two or more consecutive integers to obtain a six-digit palindrome whose first two digits are “47”. What is the sum of these consecutive integers?
(A palindrome is a number that reads the same backwards as forwards)

Answer 1

• 234

Explanation:

The number is in the form of:

• 47AA74

This is divisible by 2, can be divisible by 3 but not divisible by 4 as 74 is not divisible by 4.

So possible number of integers is 2 or 3.

Two consecutive integers

• There is no possible product ending with 4 (test it yourself)

Three consecutive integers

The numbers are x - 1, x and x + 1

The product is between 470074 and 479974

Their product is between:

• (x - 1)³ < x³ < (x + 1)³
• 470074 ≤ x³ ≤ 479974
• ∛470074 ≤ x ≤ ∛479974
• 77.75 ≤ x ≤ 78.29
• x = 78 is the only integer within this interval

Lets test:

• 77*78*79 = 474474

Sum of these:

• 77 + 78 + 79 = 234