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Distribute Numbers 1 to 99 into Five Groups
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Distribute numbers 1 to 99 in five groups so that sum of each group comes same.

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Lets first find what should be the sum in each group.

Sum of n numbers = n(n+1)/2
Sum = 99(99+1)/2 = 9900/2 = 4950
The numbers are divided into 5 groups. So sum in each group = 4950/5 = 990

Now divide the numbers into 10 groups as given below

divide 99 numbers into five groups

Merge 2 groups such that the sum comes 990
Sum of group A = 460
990 - 460 = 530 = Group H

So Group A + Group H = 990, Similarly merge other groups
Group B + Group G = 990
Group C + Group F = 990
Group D + Group E = 990
Group I + Group J = 990

The five groups are :
Group 1 : 1+11+21+31+41+51+61+71+81+91+8+18+28+38+48+58+68+78+88+98 = 990
Group 2 : 2+12+22+32+42+52+62+72+82+92+7+17+27+37+47+57+67+77+87+97 = 990
Group 3 : 3+13+23+33+43+53+63+73+83+93+6+16+26+36+46+56+66+76+86+96 = 990
Group 4 : 4+14+44+34+44+54+64+74+84+94+5+15+25+35+45+55+65+75+85+95 = 990
Group 5 : 9+19+29+39+49+59+69+79+89+99+10+20+30+40+50+60+70+80+90 = 990

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