# A number sequence in disguise

What number should replace the question mark? Explain why.

                              10051005
51005
1001005
10010010055
10055100
10051005
1005100
10051005100
?
10051005


The number that should replace the question mark is:

55100100100

Because:

Each number is composed of some sequence of 100s and 5s. If you replace these with their Roman numeral equivalents, C and V, you get:

          10051005         CVCV
51005           VCV
1001005          CCV
10010010055        CCCVV
10055100         CVVC
10051005         CVCV
1005100          CVC
10051005100        CVCVC
?              ?
10051005         CVCV

I noticed that while C and V strongly suggest consonant and vowel, one of the only words that fits the pattern CCCVV is THREE. So this is a list of the names of digits (a number sequence), with each letter replaced with C or V, and then the C or V converted from roman numerals to arabic numerals (in disguise).

          10051005         CVCV    zero
51005           VCV     one
1001005          CCV     two
10010010055        CCCVV   three
10055100         CVVC    four
10051005         CVCV    five
1005100          CVC     six
10051005100        CVCVC   seven
55100100100        VVCCC   eight
10051005         CVCV    nine

• Yup that's correct. Well done! Commented Dec 2, 2023 at 12:48
• It looked like a cipher puzzle at first! Commented Dec 2, 2023 at 14:35