Logical Reasoning: Problem Solving Strategy 1

Consider a six-sided die. From your angle, you are able to see only three faces with the numbers 14, 18, and 35 on them. The sides that you cannot see are all prime numbers. Opposite faces always add up to the same number. What are the unseen numbers?

Help us caption & translate this video!

[ejk]

Man now that I unpaused to get the answer, I feel like such a doofus 😂

[ejk]

I know the first example problem is probably super easy to a lot of ppl, but I paused the video as soon as the question was presented because I wanted to see if I could solve it. AND I ACTUALLY MANAGED 😭❤️

I'm unbearably proud of myself for this so I'm going to actually post the scratch work I was doing to solve it right here in this open comment box!

Back + 35 = Bottom + 18 = Side + 14
Back + 21 = Bottom + 4 = Side

Since Back + 21 = Bottom + 4 = Side:

Back is the smallest
Bottom is the second largest
Side is the largest

If all 3 add to 67, then
Back + Bottom + 25 = 2 × Side
Back + Bottom = 2(Side) - 25

Since smallest prime number is 1,
35 + 1 has to be absolute minimum

36 = Minimum Pair

14 + Side has to be greater than or equal to 36:

side + 14 >= 36
Side >= 22
But 22 not prime, so..

Side >= 23

(Revised) Minimum = Side + 14

Minimum Pair = 37

Bottom + 18 >= 37
Bottom >= 19

Back + 35 >= 37
Back >= 2

23, 19, and 2 are all prime, and so the answer is....!

The Die's Opposing Pairs are
[35, 2]; [18, 19]; and [14, 23]
And the number they all add to is 37!

Bottom > Back
Bottom

Back + Bottom + 25 = 2(Side)

Bottom > Back