In my left pocket I have a mix of pennies (1 cent) and quarters (25 cents). In my right pocket I have a bunch of dimes (10 cents). The number of coins in each pocket is the same, so is the cash value. What is the smallest (nonzero) number of coins I can have?

What if I had coins of x cents and z cents in my left pocket and coins of y cents in my right pocket - is there some quantitiy of coins I can have so that each pocket has the same number of coins and same cash value? (The value of the coins are positive integers x > y > z.)

CLS

x = 25: y = 10: z = 1

FOR n = 1 TO 1000
  amt = y * n
  noX = 0
  found = 0
  DO
    noZ = (amt - x * noX) \ z
    r = (amt - x * noX) MOD z
    IF r = 0 AND noZ + noX = n THEN
      PRINT x, y, z
      PRINT noX, n, noZ, amt
      PRINT 2 * n
      found = 1
    END IF
    noX = noX + 1
  LOOP UNTIL x * noX > amt OR found = 1
  IF found THEN EXIT FOR
NEXT

yields:

25            10            1
3             8             5             80
16

meaning

denomination: 25            10            1
number:        3             8            5    

value of each side:         80
total number of coins:      16

Posted by Charlie on 2009-02-17 12:00:47