Brain Teasers ? or 50 Years On........... ?

Each of the six different symbols has a different value associated with it. Adding up the value of the symbols in each row and column gives you the value for that row or column. What is the value of each symbol and what is the missing value of the column ?

BTW, I struggled with the 5x5 ticks and crosses for quite a while.....................

..............so don't give up !!

Hi Don,

I think it is:

Green Tick=7

Green X=5

Red Tick=14

Red X in Circle=20

Black Tick=28

Red X in Box=10,

with the missing row at 56.

Thanks for teasing our brains, by the way. I really like this thread.

Brilliant Mulberry.

That one took me a couple of days, on and off when I first saw it. I kept seeing ticks in boxes rather than tick in circles, Crosses instead of ticks...........

Anyway, I'm glad you and a few others, myself included, enjoy making the old grey cells move around every now and again.

We can even cope with the occasional mistake, such as with JRHardee's sandwich which took some of us old boneheads a while to get our teeth into...........

Cheers

Don

Yes, I've enjoyed the recent tick/crosses puzzles as well. To be honest, the first thing I did was replace the symbols with A, B, C etc, then the equations became much easier.

Probably stating the obvious, but the easy way to discover the missing row or column total is simply to recognise that the totals of the rows and columns must be the same. So in the recent example, the total of the columns was 318, so the missing row total must be 56 (ie to make the total of the rows equal 318 as well). Just trying to be helpful, apologies if it was so obvious it was patronising!

Steve D

Brilliant Steve, thanks for pointing this fact out. I don't think it was that obvious and certainly not patronising. I bet a few on here have gone "ah ha !" now that you pointed it out.

With the 4x4 box with just three symbols, you could almost "see" the solutions. But with the 5x5 with six symbols I eventually did what you did, used A, B, C etc and filled in the missing total using "sum of rows must = sum of columns"

Not my best diagram, I know.

Usual conditions. Frictionless pinned joints and a well greased sliding roller, again no friction !

g = 9.8 m/sec²

The system is at rest. what force F is required to keep it static.

You could give the force in Kg, but just multiplying by 9.8 gives it in Newtons and makes it look so much more difficult to a non-engineer or non-scientist

Nobody going to try the "Pulley" problem ?

I know its too simple, but it's designed to get brains into gear for the (slightly) more interesting ones to follow.

Whoops ! Sorry Frank. I didn't see your answer until just after posting. You are of course correct (even if it was simple)

..........and those piles of snowballs are beginning to melt...........

I can count, but I don't understand the question.

Frank,

Many thanks. I don't know how I managed to post such a load of rubbish.

For the sake of clarity (and embarrassment) I have deleted the rubbish version and posted what I hope is a more sensible version. The emphasis is on "hope"........

Cheers, Don

Another Thread in the Padded Cell concerns electricity generation and distribution.

Apparently (this means I don’t know how true any of this is !), but apparently about 10 years after the Grand Coolie Dam was built, new generators and transformers were installed which cut electricity wastage by 30%. 10 years later a second invention led to the installation of even newer generators and transformers that cut waste by 45% and a third invention sometime later cut waste by 25%.

How much waste was cut in total ?

A Game of Soldiers

A one-mile long Brigade of soldiers is marching back to barracks at a constant speed. The soldier at the front breaks rank to deliver a message to the soldier at the back. He marches at a constant speed, delivers the message and immediately turns and marches back to the front at a constant speed. By the time he rejoins his position at the front, the Brigade column has advanced one mile.

How far did the soldier delivering the message march ?

I have a 2-pan balance scale (a bit like the Scales of Justice) and only two weights, a 1kg weight and a 4kg weight.

You can use the weights or you can use the rice itself for weighings eg dividing a heap of rice in two.

In only 3 weighings, divide 180kg of rice into two lots, one 40kg lot and one 140kg lot.

Two identical boxes.

One is filled with 27 steel balls, the other with 64 smaller-sized steel balls. All the balls are made of the same material. Both boxes are exactly filled to the top with the balls touching the bottom, sides and top of the boxes.

Which set of balls would weigh more ?

I saw this puzzle in a book a few weeks back. The answer is obviously that both sets of balls weigh the same. [choose R=1 for the large balls, 3x3x3 balls in a cubic box of 6x6x6 units. 64 Small balls in a 4x4x4 matrix in the same box ⇒ r = ¾ etc and the arithmetic is easy)

But recalling an extremely neat Brain Teaser from a few years back. I am wondering just how you can set about proving  that there is only one way of packing 27 balls and 64 balls into same-size boxes is in a 3x3x3 matrix and a 4x4x4 matrix respectively.

I don’t have an answer and am just musing aloud………

The rice weighings

1. Divide the rice into 2 equal lots of 90kgs

2. Divide one lot of 90kgs into 2 lots of 45kgs

3. Weigh one lot of 45kgs against the 2 weights (5kgs) plus 40kgs of the other 45kg lot.

You now have a known lot of 40kgs and the balance of all the other rice will amount to 140kgs.

Spot-on SJ and a nice explanation - as usual.

Well done

cheers, Don

First goes without double checking (always dangerous!)

• Can you count - cages 7 and 14.
• Electricity waste - overall reduction 71.125%
• Marching soldiers - the soldier would march approx 2.42 miles.

Steve D

steved posted:

First goes without double checking (always dangerous!)

• Can you count - cages 7 and 14.
• Electricity waste - overall reduction 71.125%
• Marching soldiers - the soldier would march approx 2.42 miles.

Steve D

Keep on living dangerously Steve................all three correct (ok I got 2.4142 miles but we're splitting hairs )

Remind me, it was you who came up with that brain teaser to beat all brain teasers with the balls in a 5x5x10 box, wasn't it ?.............which is what got me thinking again a few post up !

The diagram shows a system of pulleys driven by belts.

The circumference of the rim of the outer pulley is exactly twice that of the inner pulley and there is no slip between belt and pulley.

If pulley A rotates at 100 rpm, how fast will pulley E rotate ?

800rpm

Nice one Mike. we'll have to start calling you "Mike the Mechanic !"..............

............on second thoughts, that might well be an insult, so we'll stick with a "well done sir"

Three symbols

Each of the three different symbols has a different value associated with it. Adding up the value of the symbols in each row and column gives you the value for that row or column. What is the value of each symbol and what is the missing value of the row ?

Not my best diagram, I know. And it seemed to get left behind on the previous page.

Usual conditions. Frictionless pinned joints and a well greased sliding roller, again no friction !

g = 9.8 m/sec²

The system is at rest. what force F is required to keep it static. The connecting rods are "light" ie you can ignore their mass.

You could give the force in Kg, but just multiplying by 9.8 gives it in Newtons and makes it look so much more difficult to a non-engineer or non-scientist