Mark:
NUMBERS
A = 6
B = 3
C = 2
D = 12 (D/B = E?)
E = 4
A - B = B so it holds that A = B + B which implies A = 2 * B.
B * C = A and because A = 2 * B it follows that C = 2.
C x C = E so 2 x 2 = E and E = 4.
C + E = A so 2 + 4 = A and A = 6.
A = 2 * B which implies that 6 = 2 * B. From this it follows that B = 3.
D : B = E so D : 3 = 4, which implies that D = 3 x 4 = 12.
So finally one finds A = 6, B = 3, C = 2, D = 12 and E = 4.
EIFFEL TOWER
1.678 meters
.
Let's call the reduction factor of the scale model x. Hence all lengths in the scale model are x times as small as in the original Eiffel tower. Therefore the volume of the scale model is x*x*x = x^3 times as small as the original volume.
The mass of an object is equal to its volume times the density of the material it is made of. The ratio between the mass of the Eiffel tower and the scale model is 7,000,000 : 1. Hence the volume of the Eiffel tower is 7,000,000 times as that of the scale model. That implies that all length scales in the Eiffel tower are (7,000,000)^(1/3) = 191.29 times as large as in the scale model. Hence since the Eiffel tower has a height 321 meters, the 1 kg scale model should have an height of 321/191.29 = 1.68 meters.
MOVING DIGIT
2^6 - 63 = 1
(In other words, 2x2x2x2x2x2, which equals 64 -63=1)
ZIP CODES
Given the criteria you provided, there are 5^5=3125 potential detour-prone zip codes. We just need to remove the ones that read the same upside down.
There are five choices for the first digit, five choices for the second digit, and three choices for the third digit. The fourth and fifth digits are determined by the second and first digits respectively. Therefore, 75 of the 3125 codes read the same upside down.
Therefore, there are 3125-75=3050 detour-prone zip codes.
Mark, your answer is an absolute joy to behold. Let it be said:
From this day to the ending of the world,
But we in it shall be remembered-
We few, we happy few, we band of brothers;
For he to-day that celebrates with me
Shall be my brother; be he ne'er so vile,
This day shall gentle his condition;
And gentlemen now-a-bed
Shall think themselves accurs'd they were not here,
And hold their manhoods cheap whiles any speaks
That joined with us upon this day.
With apologies to Will Shakespeare (1599).
Dadpad:
"Move one digit-
Its not exactly a digit but.......62=63-1
have moved the lower part of the equals sign to between the 62 and 63"
That is a most brilliant original answer, a great pleasure to read and contemplate. Have a ?'long neck' on me, and throw another shrimp on the Barbie. Let it be said:
"Remember, in an Australian pub, each person is responsible for buying a round of drinks. Never miss your turn to 'shout for a round' or you'll be branded as an American."
Ralph fell asleep in his Introductory Logic class. The teacher decides to make an example of Ralph, and slams his hand on Ralph's desk, waking him abruptly.
The instructor then quickly asks "which of the six words that I am about to give you properly completes the following sequence of words:
BASIC, ELF, HAITI, KILL, NO,
Choose from QUARTER, QUICK, QUARREL, QUAINT, QUIBBLE, and QUERY.
Much to the teacher's embarrassment
, Ralph answers the question correctly.
What "logic" did Ralph employ, and decide what the answer should be
What do you call a bunch of grandmasters of chess bragging about their Games in a hotel lobby
If you started a business in which you earned $1 on the first day, $3 on the second day, $5 on the third day, $7 on the fourth day, & so on, how much would you have earned with this business after 50 years
(Assuming there are exactly 365 days in every year)
