This week's lottery was won by a syndicate of 10 people, between them they won a total of $2,775,000. They all contributed different amounts into the syndicate and their winnings were calculated against their contributions.
If the amounts were all different but the cash step between each step remained uniform, what amount did the 2nd highest winner get, given that the sum of the lowest three amounts was equal to the sum of the highest two?
(In reply to
Answer by K Sengupta)
Since the difference between each amount is uniform, it follows that the ten amounts constitute an arithmetic sequence.
Let the sequence of 10 terms in increasing order of magnitude be as follows:
x-9d,x-7d,x-5d,x-3d,x-d,x+d,x+3d,x+5d,x+7d and x+9d........(i)
Since the total winning was $2,775,000, adding all the ten terms, we must have:
10x=2775000=> x=277500 .......(ii)
Also, by the conditions of the problem:
(x-9d)+(x-7d)+(x-5d)=(x+7d)+(x+9d)
=> 3x-21d=2x+16f
=> x=37d
Therefore, from (ii), we must have:
37d=277500=> d= 7500
Thus, substituting (x,d)= (277500,7500) in (i), we obtain the ten amounts in increasing order of magnitude as follows:
210000 225000, 240000, 255000, 270000, 285000, 300000, 315000, 330000 and 345000.
Consequently, the second highest winner received $330,000.
Puzzle Solution
