Here are sixteen problems that require the solver to use a lot of logic and just a little math...in some cases a little more math.
A mathematician and a friend were walking down a street when the
friend challenged the mathematician to tell him the age of each of
his three daughters (the ages are whole numbers).
"The product of their ages is 36" said the friend. "See the number
on that house, that is the sum of their ages".
The mathematician thought a little and said "I cannot determine their
ages".
"The oldest one plays the piano" said the friend. "OK, now I
can tell you their ages" said the mathematician.
What is the age of each daughter?
There are four people on one side of a bridge. They have only one flashlight among them. It is a rickety bridge so that only two people can be on the bridge at one time. It is dark so that the flashlight must be carried by whomever is crossing the bridge. The four people move at different speeds. One can make it across in 1 minute. One can make it across in 2 minutes. One can make it across in 5 minutes. And the slowpoke can make it across in 10 minutes. When 2 people cross, they cross at the slower one's speed. Unlike other problems like this, I won't ask you the minimum time to get all four people across the bridge. I will tell you that it is 17 minutes. There are no tricks such as throwing the flashlight or swimming etc. Nobody carries anyone else.
Now you tell me how they can do it. .
A King has 3 sons whom he loves equally. He is getting old, however, and it is time for him to appoint one of them as his successor. He calls them into his royal study and shows them 5 hats; 3 of which are white and 2 of which are black. He proceeds to turn off the light and put a hat on each of them and then hide the 2 remaining hats. He then turns the light back on and tells his sons, each of whom can see his brothers hats but not his own, that the one who can irrefutably tell him the color of his own hat will become the next King. One son sees that his two brothers both have on a white hat. He waits for either of them to say something but is greeted by silence. He then correctly tells his father the color of his own hat.
What did he say and why?
You have 2 pieces of string and a lighter. Each piece can burn for exactly one hour but they each burn at inconsistent rates (i.e. slowly then perhaps quickly then maybe slowly) so that half a piece of either string doesn't burn for exactly half an hour.
How can you tell when 45 minutes has elapsed just using the 2 pieces of string and a lighter?
There were two blind men shopping at a department store one day. Each bought 3 pairs of white socks and 3 pairs of black socks (in total they bought 12 pairs of socks). Each pair of socks was in its own package. As they left the store, they crashed into each other and dropped all the socks and mixed them.
How can each of them be sure to go home (separate homes!) with 3 pairs of white socks and 3 pairs of black socks without assistance from anyone?
You have 12 silver balls, 11 of which are identical. The 12th ball looks the same but is actually off in weight. You don't know if it is lighter or heavier but to assist your discovery have a balance scale that will enable you to weigh an equal number of balls on each side of the scale.
What is the minimum number of weighings necessary in order to determine which of the 12 balls is off in weight and whether it is lighter or heavier? And how do you do it in that number of weighings?
You have 2 equal sized glasses. One is filled up with apple juice and the other one with grape juice. You take a spoonful of the apple juice and pour it into the glass of grape juice. You then take a spoonful of the 'contaminated' grape juice and pour it back into the apple juice.
Which glass contains the higher percentage of its original juice; the contaminated grape juice or the contaminated apple juice?
Two days ago I was nine years old. Today I'm 10. Next year I'll be twelve years old.
How is this possible?
There are 1000 students and 1000 lockers in a school.
The first student enters the school and opens every locker.
The second student starts with locker 2 and reverses the state of every other locker (in this case he closes every even numbered locker.)
The third student starts with number 3 and reverses the state of every third locker. (In this case she closes some and opens some.)
This continues until the thousandth student reverses locker #1000.
After the thousandth student is done, how many lockers are open?
Imagine you are at the equator of the earth. You have a very long string which you wrap around the earth so that it touches the equator all the way around. Now you are back where you started and you take an additional 10 feet of string from your pocket and tie it to the first string, thus making it 10 feet longer. You then perform a bit of magic and make the string suspend itself above the equator so that it is an equal distance above the equator at every point around the earth.
How far above the earth will the string be suspended?
I started two watches at the same time. It turned out that one of them went two minutes per hour too slow, and the other went one minute per hour too fast. When I looked at them again, the faster one was exactly one hour ahead of the other.
How long had the watches been running?
Chuck, who lives in Issaquah, has a girlfriend in North Bend and a girlfriend in Seattle. The same number of Metro buses stop in Issaquah going to North Bend and Seattle each day. In fact, there is one per hour each way. Knowing this, Chuck decides to let fate choose which girlfriend he will visit each day. The girl in North Bend begins to tire of seeing Chuck so often while the girl in Seattle feels ignored. You see, Chuck ended up going to North Bend 5 times as often as Seattle.
Explain how this could have happened.
If 1 1/2 students can do 1 1/2 projects in 1 1/2 days, how many projects can 3 students do in 3 days?
Mr. Erdos went into a market and bought 4 items. He wanted to check the cash register so he used his trusty TI-36 but instead of pushing the + button he pushed the × button. He came up with a total of $7.11. The cashier, having added the items using the cash register also showed a total of $7.11.
What was the price of each of the four items?
This is a straight forward problem…no trick wording, all prices in dollars and cents, no fractional cents, just 4 prices that satisfy the conditions given.
Three hundred entrants are signed up for a single elimination tennis match.
How many matches must be played to determine the winner?
A fly is on the nose of Frank Shorter who is 26.2 miles from Joan Benoit. Frank and Joan begin running toward each other and as they do, the bee leaves Frank's nose and starts making a beeline for Joan's nose, flying at 20 mph. Frank runs at a constant pace of 12 mph and Joan runs at 11 mph. As soon as the bee reaches Joan's nose, he reverses and heads back to Frank, etc. The bee continues in this manner without stopping until Frank and Joan meet 1.139 hours after they start.
How far does the bee fly?