DAY437

LEFTOVERS
Credit: GAMES Magazine
May, 1983
from Mathematical Games
by Marie Berrondo

What is the smallest number which, when divided by 2, 3, 4, 5, and 6 will give the numbers 1, 2, 3, 4, and 5 as remainders, respectively?

Answer:

59..............Let n = the unknown number. Since n divided by 2 leaves a remainder of 1, n + 1 must be divisible by 2. Since n divided by 3 leaves a remainder of 2, n + 1 must be divisible by 3. Similarly, n + 1 must be divisible by 4, 5, and 6. The smallest common multiple of 1, 2, 3, 4, 5, and 6 is 60.  So n + 1 = 60, and n = 59.  

DAY 436

MONEYBAGS
Credit: GAMES Magzaine
February, 1983
Neal M. Cohen

You have $1,000 in one-dollar bills and ten empty sacks. How can you distribute the bills among the sacks so that you can provide any whole number of dollars from $1 to $1,000 merely by combining sacks? Each sack must contain at least one bill.

Answer:

There are several solutions. One is :

$1
$2
$4
$8
$16
$32
$64
$128
$256
$489