### Brain Teasers

# Ministerial Mutterings

Logic
Logic puzzles require you to think. You will have to be logical in your reasoning.

In the purely fictitious land of Fiddledeboox, the Minister of Finance emerged from a top-level meeting. Reporters had gathered to hear his announcement about either an increase or a decrease in either wages, subsidies or tax levels.

It was widely known that this Minister [M] told the truth to reporters [R] only once in every three statements.

M: Well, I can tell you that it's about subsidies.

R: Are they going down again?

M: Nothing is going down.

R: So it's good news for the people?

M: Of course. Either subsidies are going down or there will be a wage increase.

While others jostled to ask the next question, one logically minded newshound was already leaving with the hot headline news.

From the Minister's three statements above, can you also deduce the truth?

It was widely known that this Minister [M] told the truth to reporters [R] only once in every three statements.

M: Well, I can tell you that it's about subsidies.

R: Are they going down again?

M: Nothing is going down.

R: So it's good news for the people?

M: Of course. Either subsidies are going down or there will be a wage increase.

While others jostled to ask the next question, one logically minded newshound was already leaving with the hot headline news.

From the Minister's three statements above, can you also deduce the truth?

### Hint

Assume each statement, in turn, to be true. Then examine the truth or otherwise of the others.Or check the statements in the light of each of the six possibilities.

### Answer

It was a tax increase.Solution:

Remember that only one statement can be true.

If (1) is true then either (2) or (3) will be true as well. So (1) is a lie.

If (3) is true, either (1) or (2) would be also true. So (3) is a lie.

If (2) is true, it must be either wages or taxes going up or (1) would be true. It cannot be wages, making (3) true, so taxes are increasing.

There are other ways of deducing this gloomy news.

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## Comments

Jan 03, 2010

Perhaps some1 could help me with this one as I am confused. If we assume that (1) is the truth [it is about Subsidies] and that (2) is a lie [they are going up not down], we arrive at the preliminary conclusion that Subsidies are going up. Now, we must evaluate (3) as a lie to see if there is a contradiction. Before, doing that let's look at (3) in and of itself. The statement made in (3) suggests that the populus views wage increases as good and subsidy increases as bad. Therefore, if we assume that subsidies are going up, then statement (3) is clearly a lie as increasing subsidies are not good for the people and with subsidies going up they are aren't going down and wages aren't moving either way.

Oh, Rob! You should be a politician! It is taking me a while to work through your explanation! Maybe you're right - but I think you might be reading too much into the 'Of course.' That simply means that the minister wants the populace to believe that whatever he is doing will be good for them.

Hmmm ... I'll return to that tomorrow with a clear head! Anyone else?

Hmmm ... I'll return to that tomorrow with a clear head! Anyone else?

Feb 05, 2010

confusing.

Great teaser !

But I have to say that I arrived at the same conclusion as rob12345. However, I see that it was wrong now, since the going up of subsidies would necessarily make both statement (1) and (2) true [It is about the subsidies and they are going up (nothing is going down)]. The going down of subsidies, on the other hand, would make both (1) and (3) true. I think rob12345, and I, misunderstood (2) [nothing is going down -> something is going up]. IMHO

But I have to say that I arrived at the same conclusion as rob12345. However, I see that it was wrong now, since the going up of subsidies would necessarily make both statement (1) and (2) true [It is about the subsidies and they are going up (nothing is going down)]. The going down of subsidies, on the other hand, would make both (1) and (3) true. I think rob12345, and I, misunderstood (2) [nothing is going down -> something is going up]. IMHO

even i thot that Of course.. in statement 3 means that the announcement is populist, and my entire solution went kaput with that.. if 3 is false, then the measure is not populist. This means that wages cannot go up, and taxes cannot go down. Even if we remain non commital on subsidies (though, in populist terms, subsidies should go up).. this one left me confused!

I believe there will be a wage increase. Assume statement 1 is the false one so it is NOT about subsidies. so statement 2 can be true that nothing is going down. And as for statement 3, we have an "or" situation where only 1 condition needs to be satisfied to make the statement true. That condition is the wage increase. So there you have it.

Answer given is wrong (faulty logic) and this teaser was easy!

Lets look at the tax level increase as the answer says. Then 1 is false because it would NOT be about subsidies, AND 3 is false because it satisfies NEITHER of the two conditions. So how can you have two false statements? How can it possibly be about tax level increase?

Answer given is wrong (faulty logic) and this teaser was easy!

Lets look at the tax level increase as the answer says. Then 1 is false because it would NOT be about subsidies, AND 3 is false because it satisfies NEITHER of the two conditions. So how can you have two false statements? How can it possibly be about tax level increase?

Ok ok nevermind. Ignore my last post because i read the teaser wrong :-( I was thinking we needed two true statements when really we needed two false statements. The answer given is correct.

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