## Boxes

Hello all, Can someone give me a solution for this problem? There are 100 children numbered 1 to 100. There are also boxes numbered 1 to 100. Each box contains 1000 toffees. The first child takes 1 toffee from each box numbered 1,2,3,....100. The second child takes 2 toffees from each box numbered 2,4,6,....100, the third child takes 3 toffees from boxes numbered 3,6,9,...99 and so on till the 100th child. Which among the following is / are false? 1. The box left with minimum number of toffees is box numbered 64. 2. The number of boxes from where exactly 2 children took toffees is 25. 3. The number of boxes from where the number of toffees were taken as the number on the box is 2. (A) 1 & 2 (B) 1 (C) 2 & 3 (D) 1,2 & 3 Thanks in advance.

## All are true ans DCondition

All are true ans D Condition 3 : true box number 1 and 2 Condition 2 : true from box number 26 â€“ 50 Condition 1 : sum of the divisors is highest for 64 between number 1 to 100. Or you can try by simply calculating it for few boxes like Stupid example For 1st box : 1 For 2ndt box : 1 + 2 = 3; For 3rd box : 1 +3 =4 ; For 4th box : 1 + 2 + 4= 8; For 5th box : 1 + 5 =6; For 6th box : 1 + 3 + 6 =10; For 7th box : 1 + 7 = 8; For 8th box : 1 + 2 + 4 +6 + 8 =21; For 9th box : 1 + 3 +9 =13; For 10th box : 1 + 10 =11; For 1 â€“ 5 its 4, for 1 â€“ 10 its 8 And its 16 for 1-20 24 fo 1-30 Because these numbers got the highest number of divisors and their sum is always more