Got money, got 7 sons !
An old Man has some savings X.
He has 7 sons.
When he divides the Money equally between two sons one dollar is left
If he divides between three sons equally then too one dollar note is left
Similarly if he divides it equally between four, five and six sons, one dollar is left.
BUT if he divides it between seven sons equally then nothing is left.
And the obvious question is, how much money he had in the savings ?
He has 7 sons.
When he divides the Money equally between two sons one dollar is left
If he divides between three sons equally then too one dollar note is left
Similarly if he divides it equally between four, five and six sons, one dollar is left.
BUT if he divides it between seven sons equally then nothing is left.
And the obvious question is, how much money he had in the savings ?
Labels: friday special, puzzle
posted by Rajesh Lal at
9:58 PM
19 Comments:
721
2x3x4x5x6 +1
My email is drmrby@hotmail.com...email me if correct...7 dollars
61
301 :)
HE ONLY HAD 7 DOLLARS
61
lots of numbers could work
301 and 5764801 just for example
wow big numbers!
yah we found the first # that pops into head when you say multiple of 7
49!
and it worked!
yayyyy
~
x is not a multiple of 2 : x is odd
euclidian logic shows that:
x is not a multiple of 3
x is not a multiple of 4
x is not a multiple of 5
x is not a multiple of 6
x cannot be 7 as in case of 4 brother: 3 dollars are left...
the next prime number after 1,2,3,5 is 7
=> x is a multiple of 7 and not of 2,3,4,5,6
we are left with 7;
7*7 = 49
x equals 49
try it fits!!!
but 49 doesn't work...
49 / 2 = 24 with 1 left
49 / 3 = 16 with 1 left
49 / 4 = 12 with 1 left
49 / 6 = 8 with 1 left
but
49 / 5 = 9 with 4 left :(
i stick with 301 as the first possible one.
Any number that is the result of
x = 301 + 420n
where n is an integer >= 0
301 = 301 + (420 * 0) is the smallest
and 5764801 does work, of course.
7654321 is an answer.
Last digit is always 1.
Ten's digit is always even.
the first number that is not divisible by 2,3,4,5,6 and the remaining is 1 is 91.
91/2 the remaining = 1
91/3 the remaining = 1
91/4 the remaining = 1
91/5 the remaining = 1
91/6 the remaining = 1
but 91/7 = 13
It's $301.
the answer is 7
with two sons, they each get 3 dollars, plus 1 left over is 7
with three sons, they each get 2 dollars plus 1 left over is 7
with four sons they each get 1.50, plus 1 dollar left over is 7
with five sons, they each get 1.20, plus one dollar left over is 7
with six sons they each get a dollar plus one left over is 7
and with seven sons they each get 1 dollar and nothing is left over!
If you want to allow splitting of a $1, then any amount that satisfies
x = 2.80 + 4.20n
where n>=0 integer
The smallest is
2.80 = 2.80 + (4.20 * 0)
2.80/2 (with $1.00 left over) = $0.90 each
2.80/3 (with $1.00 left over) = $0.60 each
2.80/4 (with $1.00 left over) = $0.45 each
2.80/5 (with $1.00 left over) = $0.36 each
2.80/6 (with $1.00 left over) = $0.30 each
2.80/7 (with $0.00 left over) = $0.40 each
Splitting was not allowed by the puzzle however because if it was then "When he divides the Money equally between two sons one dollar is left" would never be true. With two sons there would never be any left over after dividing the money equally.
I just came across this one today. Sorry for the very late reply. The answer could be many, but the least amount he would have to have is:
{(least common multiple of 2,3,4,5,6)+1}*7
Least common multiple of 2,3,4,5,6 is 60, so the answer is 61*7=427
ANSWER : 301
-------------------------
There can be multiple answers,the smallest amount is $ 301
GOT RIGHT
-------------------------
Lillmiss, Courtney, Steve and anonymous guy above
Well it is not 49. The answers less than 1000 are 301 and 721.
I generated a table of 1000 rows, and decided to show #49 plus those that met criteria up to at least $ mod 6.
Only 301 and 721 have mod 7 of zero
$ $ mod 2 $ mod 3 $ mod 4 $ mod 5 $ mod 6 $ mod 7
1 1 1 1 1 1 1
49 1 1 1 4 1 0
61 1 1 1 1 1 5
121 1 1 1 1 1 2
181 1 1 1 1 1 6
241 1 1 1 1 1 3
301 1 1 1 1 1 0
361 1 1 1 1 1 4
421 1 1 1 1 1 1
481 1 1 1 1 1 5
541 1 1 1 1 1 2
601 1 1 1 1 1 6
661 1 1 1 1 1 3
721 1 1 1 1 1 0
781 1 1 1 1 1 4
841 1 1 1 1 1 1
901 1 1 1 1 1 5
961 1 1 1 1 1 2
hjg
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