Weekly Puzzle: Elisha’s Pen Pal

Dear Eli,

Thank you for your letter. I am excited to be your pen pal. I think it will be very fun to have a friend in the United States. Of course I have heard of New York City, it must be very exciting to live there. I live in a village called Trà Đông, in the Thiệu Hóa District, which is in the Thanh Hoá Province.

I have an older brother too. His name is Xuân. He is very nice to me. I am sorry to hear that your older brother is not nice to you. I am sure that he loves you very much and just does not know how to show it. If he is really a robot like you say maybe someone can fix his programming! Ha ha. You might be interested to know that in Vietnam we put the words in our names in reverse order, so that the family name comes first. Your name would be Manning Nelson Elisha.

I love food too! We do not eat many hamburgers here in Vietnam, but meals make me happy too, ha ha! The food here is very spicy.

I am confused by your questions about whether the pandas here know karate. For one thing, there are no pandas here in Vietnam. For another…well, never mind.

It is interesting to hear about all of your travels around the United States. Flying in an airplane must be exciting! It is too bad that everyone is trying to tackle you, though. You are right that they should be made to count to three Mississippi before they run at you.

Coach McAdoodoohead’s offensive system does sound very complicated indeed. I think it was a good idea for him to give the plays names like “GORP” and “Bug Juice” and “Swim Buddy” so they remind you of summer camp and you can remember them better.

Speaking of complicated, this is a math problem that was given to us in class. You are supposed to fill in each of the empty boxes with a number from 1 to 9 (and you can only use each number once). Can you solve it? Nobody here could. They said it was for eight-year olds, but it was too hard even for us fifth graders!

Good luck!

Your friend,
Huỳnh Văn Đồng

SOLUTION: That’s a bit of a stretch, since there’s not single solution to this puzzle, nor a consistent system for finding solutions short of using a brute force calculation on a computer. It drove me crazy for the better part of a long plane ride and then some until I finally got one of the solutions, and then quit. By the way, this puzzle is blatantly lifted from a Gizmodo post.

I actually wouldn’t encourage anyone to waste their time with this puzzle, but if you’re irrepressibly curious, here’s what I did:

1. Assumed that everything is taking place in terms of whole numbers, because come on, it’s meant for eight-year olds.

2. Established variables for all empty boxes in the puzzle in alphabetical order.

3. Summarized equation as:

a + 13 * b / c + d + 12 * e – f – 11 + g * h / i – 10 = 66

1. Squashed everything down based on order of operations, giving:

a + 13b/c + d + 12e – f – 11 + gh/i – 10 = 66

1. Dealt with the whole numbers (11 and 10), leaving:

a + 13b/c + d + 12e – f + gh/i = 87

1. Rearranged the terms a bit, leading to:

12e + 13b/c + gh/i + (a + d – f) = 87

1. That leaves us with four major groups; 12e, 13b/c, gh/i, and (a+d-f).

2. 87 is an odd number, so the combination of the four groups must include either (one even and three odds) or (one odd and three evens).

3. When multiplied, 12e will be even no matter what the value of “e” is. So the first term is ALWAYS even. All of the others can be either odd or even, depending on the values of the variables they contain.

4. With that established, the possible combinations of the four terms are as following: E-O-O-O, E-O-E-E, E-E-O-E, E-E-E-O.

5. You know what, this part is kind of dull. Long story short, you can establish that E-O-O-O is not a possibility because there aren’t many combinations that make it possible – basically you run out of odd numbers to work with so things get forced into solutions that don’t add up right.

6. Next up is E-O-E-E. In this one, 13b/c must be odd, so there are three possibilities for b/c: 6/2, 9/3, or 3/1. This means that 13b/c = 13*3 = 39, so you can subtract it out of the left-hand side leaving yourself with:

12e + gh/i + (a + d – f) = 48

1. From the above – again, it’s tedious – you can generally establish that e < 4.

2. If b/c = 6/2, you end up running out of even numbers to fill out the rest of the terms, so it’s a no go.

3. If b/c = 9/3, you can establish that e is either 1 or 2. If it’s 1, things don’t work out for some reason I don’t have very well documented in my notes. If it’s 2, you end up with the remaining digits 1, 4, 5, 6, 7, and 8 and the equation:

gh/i + (a + d – f) = 24

1. Then you just need to plug in a few of the others so you get 8*7/4 + (6 + 5 – 1) = 24

2. So a viable answer ends up being (in alphabetical order): 6, 9, 3, 5, 2, 1, 8, 7, 4.

3. Then you quit and are done with this stupid puzzle.