This. The number of people with the brilliance and hundreds and thousands of hours of dedication necessary to be IMO high performers who can’t get past an easy math IQ test is zero basically. The fact that you only have a handful of examples (of people who didn’t even qualify for the IMO, much less place) “over the years” shows your point is off-base.

Americans care less about the IMO compared to other countries for the same reason Soviets cared more about chess than all but one American named Bobby: opportunity. There are a lot more profitable and interesting ways to ply that math G and being a USAMO qualifier repeatedly or especially placing is usually enough to get one into MIT etc. and open the doors to these.

The easiest way to solve the concerns about occasional slippage or time spent studying for the AIME is give one “AIME point” for every USAMO problem solved the prior year. That handles most of the concerns about budding IMO stars missing future USAMOs.

“It is also important to note that the purpose of the AMC/AIME/USAMO is not just to select the most promising IMO team–I don’t think one could justify all the resources devoted to it, if that were the only purpose, but also to engage and inspire a large number of young students to develop mathematically.”

Also this. These tests are among the only reliable ways for students to stand out and get into Caltech and MIT to pursue lots of non-math subjects that require high math ability.

Calculus BC and the SAT are a joke and have way too low a ceiling, and the AMC/AIME are performing a crucial sorting function for all the future physicists, computer scientists, and engineers out there. This is more valuable to the US and its GDP than slightly better sorting for the one or two people who have the math IQ necessary to prove anything new these days. Those people are truly a different breed, and will find their way to a math Ph.D. with or without a cute little competition along the way.

]]>A – Anne did it

B – Bill did it

C – Caroline did it

At least one of them did it:

A or B or C = true

Solving equations (AND):

| not A xor (not A and B and not C) = true

| not B xor C = true

| not C xor B = true

| A or B or C = true

Then

| not A xor (not A and B and not C) = true

| B = C

| A or B or C = true

Simplifying xor:

(A and (not A and B and not C)) or not A and (A or not B or C) = true

false or not A and (A or not B or C) = true

not A and (A or not B or C) = true

A = false

Remembering that

| B = C

| A or B or C = true

we get

false or B or B = true

B = true

C = true

Answer: Bill and Caroline

The argument for Anne’s innocence is valid. But we can’t deduce only from Anne’s statements that Bill did it. It does follow from Anne’s statements that *if* he did it, he didn’t do it alone. Caroline is still the only other person who could have done it. So Caroline definitely did it, either alone or with Bill.

Now can prove Bill’s involvement in either of the following two ways:

1) Bill’s statement that Caroline did it is true. Therefore his statement that he didn’t do it is false.

2) Caroline’s statement that she didn’t do it is false. Therefore her statement that Bill did it is true.

If Bill’s and Caroline’s statements had been thrown out, Caroline would have been implicated in the robbery, but not Bill.

]]>Thanks for a fun puzzle! I enjoy reading your blog.

]]>I phoned to the owner of the company and I said: I’m free.

He replied Come tomorrow.

Anything else I had added would have prevented the

possibility of recruitment.

When you are looking for a job the only think that is important is to understand

what they are looking for, and to adapt yourself to the duty.

The company owner was looking for someone who can solve immediately a problem he has,

and ready to start tomorrow.

He is not interested at all on how smart you are. ]]>

Ah, Hept-$. That’s got to be 7 as in heptagon. Turns out that was all I needed!

I got the same answers as ano above so I think I am correct. I also had no recollection that -ines did not exist, (absence of evidence not being…etc.) and the problem worked out okay.

Hurrah! I did so poorly at my first problem on here, I am relieved.

Thanks for sharing Tanya – a cool propblem indeed!

]]>I must come back here more often though – great place. ]]>