MATC Mathematics Club
Problem Set Volume 3 Page

The Puzzle Corner of the MATC Mathematics Club
Madison Area Technical College
Madison, Wisconsin

Volume 3, Fall 2002 Problem Sets
Problem Set #4 ( Click here for the solutions ).
1. Using all the digits from 1 to 9, you can construct many different additions (for example, 317 + 628 = 945).  There are four such examples which have a total of 468.  Find the missing numbers.  You may not simply reverse the top and bottom numbers; new combinations must be
1XX + XXX = 468 XX5 + XXX = 468 X9X + XXX = 468 XXX + X7X = 468
2. If Susan and Neal are 10, Arabella is 20, and Jim is 5, but Richards is 10, how much is Jennifer by the same system?
3. You bought two antique lamps for $50 each.  Later, you were offered $60 for one and sold it, changed your mind when you saw its duplicate being sold for more, and bought it back for $70.  You then sold it for $80.  The first one didnāt sell at all so you reduced it 10% below what you originally paid and managed to get rid of it.  Did you make or lose money on the deal, and how much?
Problem Set #3 ( Click here for the solutions ).
1. What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second?
2. An orange costs 18 cents, a pineapple costs 27 cents and a grapefruit costs 30 cents. Using the same logic, determine the cost of a mango.
3. A substitution cryptogram is one in which each letter is replaced by another letter, number, or symbol.  For example, CAT becomes DBU when the next letter of the alphabet is substituted.  Solve the following: SV DSL RH GLL HSZIK HLNVGRNVH XFGH SRNHVOU.
Problem Set #2 ( Click here for the solutions ).
1. At the 2001 Wisconsin State Fair a vendor was "hawking" a fair special.  If you buy one pair of sandals at the list price of $25, you get a second pair at a 40% discount, and a third pair at half price.  If you take advantage of the fair special and purchase three pairs of sandals, what percentage do you save off the regular price?
2. Suppose that a, b, c, and d are four distinct numbers where b + c = a, ad = a, d + a = d, b(a + d) = d and b ö c = d. Find d.
3. EVE/DID = .TALKTALKTALK... represents a common fraction written as a repeating decimal.  What is the fraction?
Problem Set #1 ( Click here for the solutions ).  
The three problems below on Alphametics (also known as Alphanumerics or Cryptarithms) are puzzles in which letters are substituted for the digits in an arithmetical calculation. Some of the problems may have either unique or multiple solutions.



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