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/sci/ - Science & Math

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2322127 No.2322127 [Reply] [Original]

Hey, /sci/! Need a little help with this interesting exercise:

How many 10-digit numbers are there, where you can "erase" two neighbouring digits, so you get a number 99-times smaller that the original one.

Thank you so much!

>> No.2322147
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2322147

POTATOE!

>> No.2322176

bump

>> No.2322200

I see no obvious methods do calculate this beside bruteforcing it.

>> No.2322210
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2322210

>>2322200
POTATOE!

>> No.2322214
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2322214

This is now a wallpaper thread

>> No.2322218
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2322218

>>2322214
POTATOE! :D

>> No.2322224
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2322224

>> No.2322223

It has to be a 10-digit number divisible by 99.

So you have two constraints on the sum of the digits of said number (9-divisibility implies that sum of digits = multiple of 9, if I remember correctly) (11-divisibility implies that the sum of odd-positioned digits minus the sum of even-positioned digits equals 0 or a multiple of 11).

It's a start.

>> No.2322222
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2322222

>> No.2322227
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2322227

>> No.2322240
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2322240

>> No.2322248
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2322248

>> No.2322664

bump

>> No.2322687

do you count things like 0000000001 as a ten-digit number?

>> No.2322744
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2322744

50

>> No.2322753
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2322753

>>2322744

1039500000
1138500000
1237500000
1336500000
1435500000
1485000000
1534500000
1633500000
1732500000
1831500000
1930500000
2029500000
2128500000
2227500000
2326500000
2425500000
2475000000
2524500000
2623500000
2722500000
2821500000
2920500000
3019500000
3118500000
3217500000
3316500000
3415500000
3465000000
3514500000
3613500000
3712500000
3811500000
3910500000
4009500000
4108500000
4207500000
4306500000
4405500000
4455000000
4504500000
4603500000
4702500000
4801500000
4900500000
4950000000
5445000000
6435000000
7425000000
8415000000
9405000000

>> No.2322955

cool :) is there some calculation, or just logical thinking?

thanks anyway!