Maths question! Try to solve it :)?

Question

The sum of the digits of the number 2004 is 6. How many whole numbers from 1000 to 9999 have 6 as the sum of their digits?

Answer 1

1005,1014,1023,1032,1041,1050
1104,1113,1122,1131,1140
1203,1212,1221,1230
1302,1311,1320
1401,1410
1500
For 1000s: 6+5+4+3+2+1 = 21

For 2000s: 5+4+3+2+1=15 numbers
For 3000s: 4+3+2+1=10 numbers
For 4000s: 3+2+1=6 numbers
For 5000s : 2+1=3 numbers
For 6000s : 1 number
No further such numbers:

Total no. of such numbers b/w 1000-9999: 1+3+6+10+15+21 = 56

Answer 2

5

Answer 3

let four digits are x, y, z, w
where x is at thousands place
then we have
x + y + z + w = 6
with the condition that
0 < x <= 6, 0 <= x, y, z <=6
then we have to find the number of positive integral solution of above equation, which is equal to
coeff of p^6 in (p + p^2 + ...+ p^6)(1 + p + p^2 + p^6)^3
i.e coeff of p^6 in p(1 - p)^-4
i.e coeff of p^5 in (1 - P)^-4
which is equal to 4.5.6.7.8/1.2.3.4.5 = 56

Answer 4

from 1000 to 6000 ( hah - I was listening!)

I counted 41 (revised)

1230, 1203, 1023, 2130, 2103, 2013, 3120, 3102, 3012,
1320, 1302, 1032, 2310, 2301, 2031, 3210, 3201, 3021,
2400, 2040, 2004, 4200, 4020, 4002, 6000 (25 to here)
1122, 1221, 1212, 2211, 2112, 2121, 1113, 1131, 1311,
3111(35)
5100, 5010, 5001, 1500, 1050, 1005(41)

Answer 5

400

Answer 6

Lee Holmes deposited $15,000 in a sparkling decrease fee expenses account at 9% interest compounded semiannually. on the initiating of 365 days 4, Lee deposits an added $40,000 at 9% interest compounded semiannually. on the top of 6 years, what's the steadiness in Lee’s account?

Answer 7

101 whole numbers