“Club Math” is the first ever student math club at Kaua‘i Community College. The club is interested in the practicality and usefulness of mathematics in everyday living. The primary goal is to involve the community by promoting this ideal. What
“Club Math” is the first ever student math club at Kaua‘i Community College. The club is interested in the practicality and usefulness of mathematics in everyday living. The primary goal is to involve the community by promoting this ideal. What follows is last week’s math puzzle followed by the answer.
The club will submit weekly brainteasers for the education page. The following week, the answer will be provided.
An unusual year:
The year 1978 has an unusual property. When you add the 19 to the 78, the total is the same as the middle two digits (97). What will be the next year to have this same property?
Solution:
1) Although this is a game of “Guess and check”, there is a strategy. First off, the sum of the numbers cannot exceed 99 (because there are only two digits in the middle). Secondly, the outside digits need to be close enough together so that they do not exceed the middle number when added. Thirdly, they need to be far enough apart so that they do not fall short of the middle number when added. From there, have fun.
2) While I was beating at it, I came up with a slightly confusing strategy to try and narrow it down … If we assign each digit of the year a variable we can hopefully make things easier. We’ll let them equal A, B, C, and D respectively. This is by no means any conventional formula. There are two key aspects to be noted: We’re adding the first two and the last two numbers to get the middle two numbers (A B + C D = B C) and that the middle numbers are B and C.
When we replace B and C with any numbers, we can simply complete the addition problem to solve for A and D to figure out the year. When we reassemble the year in the same order, we get 1978. Now, to find the next year… We know B C has to be less than 100 and it must be after the year 1978, so after some trial and error, we get 2307.
This week’s
brain teaser
Augustus De Morgan:
“I was X years old in the year X-squared.” Augustus De Morgan said this in the 1800s. When was he born?