+0

# How many 5-digit numbers satisfy the following conditions:

+1
133
4
+272

How many 5-digit numbers satisfy the following conditions:

The number contains only digits 1, 2, 3, 4, 5.

The number starts with 1, 3, or 5.

Each pair of adjacent digits differs by exactly 1.

For example, 32343, 12345, 54545

Jan 29, 2021

#1
+120023
+2

Here's what I get......

1   2    1    2      1

1   2    1    2      3

1   2    3    2      1

1   2    3    2      3

1   2    3    4      3

1   2    3    4      5

3   2    1    2      1

3   2    1    2      3

3   2    3    2      1

3   2    3    2      3

3   4    3    4      3

3   4    5    4      5

5   4    3    2      1

5   4    3    2      3

5   4    3    4      3

5   4    3    4      5

5   4    5    4      3

5   4    5    4      5

Did I miss any  ???

Jan 29, 2021
#3
+1

i think there are more to write...

Guest Jan 29, 2021
#2
+2

total nos=24.

but, some glitches in my code. can anyone spot it?

12121

12123

12321

12323

12343

12345

32121

32123

32321

32323

32343

32345

34321

34323

34343

34345

34543

34545

*34565

*34567

54321

54323

54343

54345

54543

54545

26

python code#

total=0
f=[0]*5
for i in range(12121,54546):
temp=i
for j in range(5):
f[j]=temp//(10**(4-j))
temp%=(10**(4-j))
#print(f[0])
if f[0] in range(1,6,2):
flag=0
for k in range(1,5):

if f[k]>0 and abs(f[k]-f[k-1])==1:
flag+=1
if(flag==4):
print(f[0]*10000+ f[1]*1000+ f[2]*100+ f[3]*10+ f[4])
total+=1
flag=0
print(total)

Jan 29, 2021
edited by Guest  Jan 29, 2021
edited by Guest  Jan 29, 2021
edited by Guest  Jan 29, 2021
#4
+1

12121 , 12123 , 12321 , 12323 , 12343 , 12345 , 32121 , 32123 , 32321 , 32323 , 32343 , 32345 , 34321 , 34323 , 34343 , 34345 , 34543 , 34545 , 54321 , 54323 , 54343 , 54345 , 54543 , 54545 , Total =24 such numbers

Jan 29, 2021