Are You Smarter than a First Grader? (2)

1st grader 1

My brother sent me two math exam questions, supposedly grade 1. Let’s see if you are smarter than a first grader.

(Q1) ABCD X 9 = DCBA. Each of the 4 alphabets A, B, C, and D represents a different digit. What’s A, B, C and D?
(Q2) AB – CD = EF, EF + GH = PPP. Each of the 9 alphabets represents a different digit. What are A, B, C, D, E, F, G, H and P?

As far as I can remember, algebra wasn’t taught until high school. But that was over half a century ago. Maybe today’s kids are much smarter. But for Q1, there are 4 unknowns and only one equation. For Q2, there are 9 unknowns and only 2 equations. You need as many equations as the number of unknowns, so how do you solve the problem algebraically? Algebra won’t work in this instance. But a little logic might.

In Q1, the reasoning could be as follows:
* Each of A, B, C, D could be any unique number between 0 to 9.
* For a 4 digit number ABCD to be multiplied by 9 and still remain to be 4 digits, A can only be 1. It cannot be >1 as then the product would be 5 digits, not 4. A cannot be 0 either as then BCD X 9 could not produce a 4-digit number ending in 0.
* So for now we have 1BCD X 9 = DCB1. But the only multiple of 9 that produces a number ending in 1 is 9 i.e. 81. Therefore D = 9.
* Now we have 1BC9 X 9 = 9CB1, and B, C, could be 0, or a number between 2 to 8.
* But if B is any number between 2 to 8, when multiplied by 9 it would carry over from “hundreds” to “thousands”, which is not permissible by the previous steps. Hence B can only be 0.
* Now we have 10C9 X 9 = 9C01, with C being a number between 2 to 8.
* By trial and error, the only number that fits is 1089 X 9 = 9801. Therefore C = 8.

That’s a fair bit of logical and arithmetical thinking. Do we expect that from a first grader, a six-year old? And if you think that’s hard, try Q2. Any math teacher out there who can offer some help?

Exposé of Hong Kong Riot

If you understand Cantonese, my brother has done an excellent analysis of the factors behind the riot in Mongkok, Hong Kong during Chinese New Year (Part 8).

Part 9 digs deeper to review psychological war tactics, using Ukraine as an example. It dissects the forces behind what’s happening in Hong Kong, a chess piece in the struggle between the US and China for supremacy. Parts of the video is in English.

Things are not always what they appear on the surface. Tough times are coming. Watch and pray, and be prepared.