Question

Modified P.E question:

Working from left-to-right if no digit is exceeded and not equal by the digit to its left it is called an increasing number; for example, 134568.

Similarly if no digit is exceeded and not equal by the digit to its right it is called a decreasing number; for example, 65420.

We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.

What is the total number of non bouncy numbers?

Here is a similar question with more details : https://projecteuler.net/problem=112

Answer 1

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Answer 2

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Answer 3

By your modified definition, is the first bouncy number 11 ?

Answer 4

yep that is true

Answer 5

Binary?

Answer 6

nope, i think the question is number system sensitive

Answer 7

hey look at this pattern for the number of none bouncy numbers from 10 digit to 1 digit it follows this patternn

Answer 8

for 10 digit
solving the equation
a1+a2+a3+....+a9=k , where k E { 9}
where a_n >= 1

for 9 digit
solving the equation
a1+a2+a3+....+a8=k , where k E {9,8,8}


for 8 digit
solving the equation
a1+a2+a3+....+a7=k , where k E {9,8,8,7,7,7}

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Answer 9

and then we got this general formula

a1+a2+....+an = k
a_m >=1

number of solutions to this must result from
1+1+...+(1+k-n)=k
#of Solutions=k-n+n-1 choose n-1
=k-1 choose n-1

Answer 10

lavosh Danial will see in morning -.-

Answer 11

oh actually it might not be too much work from here to see how many non repeating numbers are there to cover the actual peuler question