You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?
First weigh three coins against three others. If the weights are equal, weigh the remaining two against each other. The heavier one is the counterfeit. If one of the groups of three is heavier, weigh two of those coins against each other. If one is heavier, it’s the counterfeit. If they’re equal weight, the third coin is the counterfeit.
Cornelius got a flat tire on a miserable, rainy day. As he was changing it on the side of the road, he placed the four lug nuts in the overturned hub cap. As our dear friend was moving back to put on the spare, he accidentally bumped the hub cap. He watched helplessly as all four lug nuts rolled into a deep sewer and were whisked away. Then our friend had a brilliant solution and within minutes was driving safely away.
The name ABRAHAM can be changed into a word for a primitive musical instrument by replacing each letter with a different letter. The repeated letters (A is this case) must be replaced with the same replacement letter in the new word.
1. Each letter represents a different digit from 1 to 9
2. The total of each row is 17.
3. (B × B) + B + F = A
4. C × F = EF (a 2-digit number, not their product)
A + B + C = 17
D + E + F = 17
B2 + B + F = A
C × F = EF
To begin with, B has to be a 1 or 2 or else A wouldn’t be a single digit. Plug in B = 2, gives you 6 + F = A, meaning F and A can only be (1,7) or (3,9). To get 17, C would have to be 8 or 6, but those values don’t work for C × F = EF. So B must be 1.
2 + F = A means F and A can be (2,4), (3,5), (4,6), (5,7), (6,8) or (7,9). To get 17 on the top row, the only option that leaves C as a single digit is F = 5 and A = 7.
C × F = EF
9 × 5 = 45, so E = 4 and D = 8 to make the second row equal to 17.
Fence. Fences keep ne’er-do-wells out and protect people inside. A fence is a person who buys stolen goods to later resell them for a profit. Those who fence practice the sport of fencing. En garde! And people don’t like it when you sit on the fence in a heated debate. (Believe me, I speak from experience)