Mental Nuts-- Can You Crack 'em?
 

Mental Nuts-- Can You Crack 'em?
This is a little book of puzzles, riddles, math problems and the like published in 1921 by Waltham Watch Co.
There are 100 Mental nuts, though the first two are just nifty number tricks. Pay careful attention to what is being asked, a number of these puzzles turn on verbal assumptions.

I will put up a new mental nut every day only if the previous nut is cracked or you all cry Uncle. From time to time I will also post some of the advertisements inside the book.

Here is the first (actually #3) Mental Nut:

Doesn't matter how I arrange them ... all whole numbers are divisible by seven ... doesn't say it has to be evenly divisible.

63/1

6 - 3 - 1

Except that #6 walks on his hands which forms the number 931.

931 / 7 = 133

wait a minute....

This is an unsolvable problem.

We don't know how fast the trains are going.

Doesn't matter if they're on a treadmill.

Rhianne FTW!

Rhianne wins this round. I will keep score.

I am way too distracted by that cover design to figure out teh puzzles. It's super modern for 1921!

I thought this was a thread about me. :(


MORE MENTAL NUTS! I can never get them but it's fun trying.

Today's Mental Nut. You are only allowed to google what currency was in circulation in 1921.

$2 bills

show your work

I would like a beautiful clock catalog mailed to me, please.

The conductor has only three-cent pieces, but he has lots of them. 165 three-cent pieces make change from a $5 bill for a $0.05 fare. This hoard of coins can't make the right change for a $1 bill though.

In circulation in 1921 US currency.

??

In the 40 years up to 1921, over a million of them were minted. Surely the conductor could have accumulated 165 of them.

I will recalculate with whatever was available starting in 1921, if that is what you're getting at.

V, that's a fascinating link. I didn't know trimes existed... but I have heard of tribles. ;)

Did you notice that back then postage rates were going down, not up ?
Maybe it was before businesses got the $ reduced junk mail rates. :eyebrow:

Was any currency in postage stamp form?

there was, but I can't "show my work" for the same kind of problem describe in footfootfoot's post for making change.

In circulation, not, in the conductor's pocket

Thomas Edison and Henry Ford proposed some kind of 'electric currency' in 1921. Supposedly.

Don't ask me, I don't understand the article:

http://eddiesblogonenergyandphysics....ty-backed.html

coins minted thirty years earlier were almost certainly "in circulation". then you say "in 1921 currency". Are you saying the change was rendered in currency minted in 1921? We've strayed a bit from the paragraph in your book. I reckon there are multiple answers to the puzzle, I think I've offered one valid one, though perhaps not the one in your book. I'll hang on until I have an epiphany or you offer the / a different solution.

:)

...

The solution is a practical one, not relying on conductors carrying vast numbers of discontinued coinage.

Does it have something to do with the value of silver?

Just an aside (I am completely stumped by this) I remember using shilling and two shilling pieces as a child. They were accepted in lieu of 5p and 10p coins. But the country decimalised before I was born.

So I understand that the question has a more elegant answer than V suggested, but the words "in circulation" still include discontinued coinage in my head.

I know what you mean and what V means, and I have mosquitoes in my basement still but that doesn't make it summer.

Big V was very close with his wikipedia search, and apart from the coins being discontinued and British, Sundae is also close.

Out of the mouth of babes and fools....

showing my work, if not an answer...
 

At first glance, I see this as a problem of how to make $4.95 change and not be able to make $0.95 change.

Some assumptions I make:

This transaction is being conducted (ha) in US money.

I am disregarding the idea that the "change being made" would be in some weird scrip from the trolley line, counting out a book of tickets equal to $4.95 for example. I don't count this as "money he had".

I'm assuming the passenger is only paying 5 cents for his ride. And that he does ride and he does pay and he does get change.

Hm, that's a lot of assumptions. Maybe the passenger says, "Ok, here's a nickel." But that doesn't answer the question "what money had he?". It makes the problem silly.

a passenger on a trolley (he has to pay). offers a $1, expecting 95c. change. conductor can't make 95c change. I hope this isn't part of the "trick". this sounds really plain. The conductor says he can make $4.95 change.... does he? he says he can make change for a $5 bill tendered for a 5c fare. Am I making an unfair assumption? I am not being literal in the recounting of the parameters, but that's where the cleverness of the puzzles hides...

It's a good puzzle.

to my mind, discontinued in the wiki article means no longer minted. not out of circulation.

Now I sound snippy. I'm not, I'm just wrestling with this one.

So it has nothing to do with the value of silver.

OK, thanks.

I didn't mean to challenge the answer - it's a good question that needs thinking. V is thinking, I was rambling.

I call Uncle, but I'm impatient.
I'd expect you to ask for a quorum of at least five (shillings).

Could the answer involve the phrase "I cannot make the change"?

The passenger is attempting to exchange Canadian Dollars for US ones - the fee for which is more than $1?

If so, then the answer to the actual question asked would be: Canadian money.

Answer here:

http://en.wikipedia.org/wiki/Quarter_eagle

ORLY?

Show your work, please.

eta:

Meaning he has coins only to change $5 bills and multiples thereof? Ok, I see that. But that's not really the plain meaning of making change for a dollar (or five dollars) when tendered for a fare. If I've dramatically missed the emphasis, tell me. Was the question, what can make change for 5s and not 1s?

So, the Quarter Eagle is $2.50, meaning the conductor must still produce $2.45. Two $1 bills, four dimes and a nickle, and being a ratshit conductor that is all he has.

That looks good to me ZG.

I agree, tha's change for $5, and not for $1. So is my answer, too.

I'm calling that last nut unsolved. And V, I'll tell you the same thing I told my students: If you put half the effort into finding the correct answer that you put into defending your incorrect answer you'd be at the top of the class.

Technically, perhaps correct, but Occam's Razor says "BZZZZZZ! Thank you for playing."

Here are 5 and 6 since I was out deer hunting all day yesterday. (No)

DOMFCOTL,ISN.

If the answers to number 5 all have to be whole numbers, then:
Dad = 35
Ma = 30
Bro. = 8
Me = 10

If fractional ages can be included (and why couldn't they?), then dad can be anywhere between about 31.5 and 38.5.

The answer to number 6 depends on whether B gets his first increase after 6 months or after 1 year.

What? Maybe I'm missing some glaring issue, but this one doesn't even seem like a puzzle to me...

..................A.........B
At hire:....$500....$500
6 mos:....$500....$525
1 year:....$600....$550
1.5 yr:....$600....$575
2 year:....$700....$600

...There are no percentages to contend with, B is just getting less money.

The guy getting 25 every six months is receiving more INCREASES. ;)

Sure, I suppose B could have been hired decades ago, so at any single given point in time he will still be making more than A. But that's dumb.

It doesn't ask who gets more money. It just asks who receives the most.

The most increases is B with two increases every year followed by A who only gets one increase per year.

Clerk B gets most money in the first year but after that Clerk A takes the lead. I think I must be missing some point.

Assume both A and B get paid half a year's salary at the end of every 6 months; here's the totals for 3 years:

I was thinking along those lines, but remember, B's increase is $25 per year, received every six months. So for the second half of the first year B gets an annual rate of 525, which when /2 is 262.50, not 275.

ETA:

Attachment 36035

After 6 months they are even. After 12 months B is ahead. After 18 months A takes the lead and stays there.

I thought about that, but it's not clear from the wording.

True, there is ambiguity, but I think this is the most natural interpretation. Your sums are consistent with the other interpretation.

Yeah. Dammit.

You can put a cat in the oven, but, that don't make it a biscuit.

I don't know what that means, I just wanted to toss out another clever phrase.

OK, HLJ gets the various family member's ages right. The question of the two clerks has me a bit stumped and I have the answer from the book, but not the explanation.

The Answer is that "B receives $25 more per year than A"

I think part of the nut is remembering that you aren't paid before you work. And the other part is the somewhat sneaky wording "and B gets a $25 increase every six months" That doesn't mean that B is earning .5*500 for the first six months, then .5*525 for the next six months, while A earned 1*500 for 12 months.
It means that B gets 250 and then 275 as HLJ shows.

So I'm going to give him the points for this one.

The scores so far
Rhianne:1
HLJ: 2

Next nut coming up shortly.

My answer is better.

Now I just have to fit it in the box. ;)

OK, try this one:

$14.00

Bad $10 bill and a $4 pair of shoes

20 bucks.

Infi wins this one.

$4 shoes
$6 change
$10 make good on bad bill

$20.

Butt the shoes sold for $4.00. Surely they didn't actually cost him that much.
There would have been profit involved for the shoemaker.
Then again I guess we are talking opportunity cost ...

just bustin' on ya.