George likes to play with marbles. He has got a jar full of marbles of different colours. One day, he started to pick the marbles out of the jar. In the first picking he took away 1 marble, in the second picking he took out 2 marbles, in the third he took out 3 marbles from the jar - each time picking up as many marbles as the number of picking. He found that after fifth and seventh picking, the number of marbles that were left in the jar was a perfect square. Now, can you find the number of marbles that was in the jar at the beginning?

 

64 marbles

less (1+2+3+4+5=15)
64-15=49=7*7

less (1+2+3+4+5+6+7=28)
64-28=36=6*6

 

BTW - after 10 picks also a perfect square

+1.

 

 

x = marbles after day 5

x-13 = marbles after day 7

 

if x = 49

x-13 = 36

 

49+5+4+3+2+1 = 64

 

Ok, I would put in the answer but I don't know how to use spoilers. But I'll give my method.

The difference between 2 squares is always a+b. A being the previous perfect squares square root, the second being the new perfects square square root. Its hard to explain either way, on the fifth one he's taken out a total of 15. The 6th and 7th would 28. So the square with 13 between it and the next one can be found. Which leads to the answer. Using algebra, not simply taking guesses. I think.

The first two squares have a difference of 13, That would be 36 and 49,marbles at start is 59.

The first two squares have a difference of 13, That would be 36 and 49,marbles at start is 59.

 

Nope. 59 less 5 picks (5+4+3+2+1=15) is 44 not 49.