Good afternoon, dear guests!
One of the interesting comments on my article "Math Test for Teachers in the USA "was a review with the attached problem of Henry Ford, which prompted me to describe this puzzle.
Henry Ford (07/30/1863 - 04/07/1947) - car tycoon and former owner of a series of car factories. He quickly gained popularity due to unconventional approaches to his business. The FORD automobile plant specialized in inexpensive cars under the slogan "cars for everyone." The Ford Motor Company still exists today.
So to the challenge: Since Henry was selecting people with a mathematical mindset, this puzzle was one of the questions asked when interviewing for the position of a senior engineer at Ford. After 2 years, no one solved the problem in 15 minutes, Henry published it in the newspapers as a curious incident.
The task sounds like this:
There are three names on the card presented. Each letter corresponds to one digit from 0 to 9, where it is known in advance that D = 5. Find the rest of the letters and numbers, following all the mathematical rules of addition:
While you're thinking, I'll tell you a little more about Henry :-)))
Henry Ford was the founder of Detroit Motor Company, later renamed Henry Ford Company. During this period, he developed and patented his own mechanical gearbox with a planetary gear shift principle. Subsequently, it gave way to the development of the Frenchman Louis Renault, which is still used today.
Ford has cut the assembly line time of the car from 12 hours to 90 minutes, thus gaining an economic advantage in the competition between automakers. Reducing the time allowed to reduce the price of cars, which later became available to the average population.
Ford introduced an 8-hour workday at its factories and introduced a reward system for sober lifestyles.
In addition to his passion for the automotive industry, Henry Ford patented 161 more inventions, which you can find on the Internet, but since this is not the topic, let's move on to solving the problem ...
Solution sequence
There are many algorithms for solving, and one of them is described below. There are a lot of assumptions in the solution process, so in order to reduce the scribbling, we immediately move along the correct logical chain:
1) So, the first place is the ones place: If D = 5, then adding D + D we get 10, i.e. T = 0, and 1 is stored to add the tens digit.
2) Last bit: Since D (5) + G = R, then R> 6, and also R is odd, since when adding the tens digit L + L + 1 (remainder of 10) = R. There are only two odd numbers between 5 and 9: 7 and 9. If you choose 9, then at the 4th step all calculations collapse, so we immediately take R = 7. If R = 7, then G = 1 or 2, because we don't know if O + E is more or less than ten.
3) So, R = 7, so these are numbers 7 or 17. We make up the equality: L + L + 1 (remainder) = 7 or 17. If we choose 7, then at the 6th step we come to a dead end. We assume that L + L + 1 = 17, then L = 8. (As a result, we have the following occupied numbers: 5,7,8)
4) We look at the 3rd category: A + A + 1 (the remainder of 17) = E. We assume that A = 4, then E = 9. (Already getting busy: 4,5,7,8,9)
5) Let's substitute E = 9 in the 5th digit and get O + E = O, O + 9 = O (+1). We still have free numbers: 1,2,3,6. Substituting each into this equality, we get the only true case when O = 2. those. 2 + 9 + 1 = 12.
6) Then D + G + 1 = R, 5 + G + 1 = 7, therefore: G = 1.
7) There remains the 4th digit and free digits 3 and 6: N + R = B. Therefore, N + 7 = B, and 6 + 7 = 13, where B = 3.
Resolved!
For me, 15 minutes is a really short time to go through many options, and there must be a fairly high IQ to solve such a puzzle.
Thanks for attention!
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