# 5 Classic Math and Logic Puzzles

TR Smith is a product designer and former teacher who uses math in her work every day.

Here are five classic logical brain teaser puzzles that require some mathematical knowledge, but mostly logical reasoning skills. Some of these you may have seen before in simpler forms, so if you know how to solve the easier version, you may be able to figure out the harder version too. Some hints and the full solutions and explanations are in the companion article, Hints and Solutions to the 5 Classic Logic and Math Puzzles. See how many you can figure out with looking at the hints.

## Logic Puzzle 1: Limited Use of Balance Scales

Wesley has 29 coins of identical size and shape; 28 of them are solid gold and one is made of a cheaper and slightly heavier material. Wesley can't tell by the look of the coins or by the feel of them which one is the fake.

Anne will let Wesley use her balance scale to discover which coin is counterfeit, but with the catch that he can only use the scale at most four times for free. If he needs to use it more than four times, he has to pay her some of his coins. Can Wesley find the fake coin without paying Anne, and if so, how?

## Logic Puzzle 2: Rickety Bridge Crossing

Four friends -- Wanda, Xavier, Yolanda, and Zack -- are traveling at night and they need to cross a long and very rickety bridge. The bridge can only hold at most two people at a time, and because it is pitch black outside and the bridge has holes, they absolutely need to use a flashlight to cross it safely.

Wanda can cross the bridge in 1 minute, Xavier can cross it in 2 minutes, Yolanda can cross it in 6 minutes, and Zack can cross it in 8 minutes. If they only have one flashlight among them, how can they cross the bridge in 15 minutes?

## Logic Puzzle 3: Extreme Arithmetic

Using nothing more technologically advanced than a pocket calculator, can you verify if following arithmetic is correct?

123456^17 + 654321^17 = 5213281192281563766701593^4

Here the ^ stands for exponentiation. The equation is shown below in standard math type.

## Logic Puzzle 4: How Old Is Great Uncle Francis?

At a family reunion, two young cousins Alison and Bethany are talking to their Great Uncle Francis. They want to know how old he is, but instead of telling the young girls directly, he writes down a list of 10 possible ages, with one of the numbers is his true age:

65, 67, 69, 76, 78, 84, 87, 94, 95, 96

The girls are too young to tell the difference between a 65-year-old and a 96-year-old, so they ask him for a clue. Francis whispers the first digit of his age in Alison's ear, and the second digit of his age in Bethany's ear, and challenges the girls to figure out his age without swapping the information they just received.

Alison says, "I can't figure out how old Great Uncle Francis is, but I know Bethany doesn't know either."

Bethany says, "At first I didn't know how old he was, but now I do."

Alison says, "Well, now I know too."

How old is Great Uncle Francis and how did the girls figure it out from their brief conversation.

## Logic Puzzle 5: How Old Are the Girls?

Tom and Jim get together for some beers after many years of not seeing each other. Tom asks about Jim's family and Jim says he has three daughters. When Tom asks how old they are, Jim says the product of their ages is 144.

Tom says that's not enough information to figure out their ages, so Jim tells him that the sum of their ages is the street number of the bar.

Tom goes outside to look at the address of the bar, comes back, thinks for a while, and tells Jim that's still not enough information to deduce their ages.

Jim tells Tom that when his oldest daughter was 6 years old, she drew a picture of her two younger sisters that Jim still keeps in his office.

Tom thinks for a while and tells Jim that he still doesn't have enough information. Jim then tells Tom that his youngest daughter loves to play hide and seek with her older sisters.

Finally Tom says that he has figured out their ages. How old are Jim's three daughters?

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