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## Mensa Mind teaser

on Sun Dec 24 2017, 19:02

**First topic message reminder :**

1}I know MYG likes a puzzle so specialy for her and everyone else of course.

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

2}Take 9 from 6, 10 from 9, 50 from 40 and leave 6.

How Come ??

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 20:37

A group of cyclists ride from one town to another.

On the first day they cover one third of the total distance. The next day they cover one quarter of what is left. The following day they cover two fifths of the remainder and on the fourth day half of the remaining distance.

The cyclists now have 20 miles left.

How far have they travelled?

On the first day they cover one third of the total distance. The next day they cover one quarter of what is left. The following day they cover two fifths of the remainder and on the fourth day half of the remaining distance.

The cyclists now have 20 miles left.

How far have they travelled?

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 20:44

I'm changing the thread title as we are past christmas It will become Mensa mind teasers

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 21:13

Let L = length of journey.

Day one distance covered = 1/3L

Day two distance covered = ¼ x 2/3L = 1/6L

Day three distance covered = 2/5 x 1/6L = 2/30L

Day four distance covered = 1/30L

1/3L + 1/6L + 1/15L + 1/30L = L - 20

10/30L + 5/30L + 2/30L + 1/30L = L - 20

18/30L = L – 20

18/30L + 20 = L

18/30L + 12/30L = L

Therefore 20 = 12/30L

Therefore L = 600/12

L = 50miles

I think the answer is too low.

I suspect my maths has let me down.

I hope there is some logic to my method.

Day one distance covered = 1/3L

Day two distance covered = ¼ x 2/3L = 1/6L

Day three distance covered = 2/5 x 1/6L = 2/30L

Day four distance covered = 1/30L

1/3L + 1/6L + 1/15L + 1/30L = L - 20

10/30L + 5/30L + 2/30L + 1/30L = L - 20

18/30L = L – 20

18/30L + 20 = L

18/30L + 12/30L = L

Therefore 20 = 12/30L

Therefore L = 600/12

L = 50miles

I think the answer is too low.

I suspect my maths has let me down.

I hope there is some logic to my method.

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 21:21

I may have to rethink.

My maths is for the distance between the towns, not the distance traveled.

My maths is for the distance between the towns, not the distance traveled.

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 21:26

You are miles out. Up a bit.

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 21:32

@raymyjamie wrote:I may have to rethink.

My maths is for the distance between the towns, not the distance traveled.

Or is it!!!!!!?

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 22:21

Another try:-

Let 'L' be total distance.

Day one distance covered = 1/3L

Day two distance covered = ¼ x 2/3L = 1/6L

Day three distance covered = 2/5 of remainder = 2/5 x L – (1/3L + 1/6L) day one and day two distances subtracted from total distance L

= 2/5 x L – (1/2L)

= 2/5 x 1/2L = 2/10L = 1/5L

Day four distance covered = 1/10L half of day three

1/3L + 1/6L + 1/5L + 1/10L +20 = L

10/30L + 5/30L + 10/30L + 3/30L + 20 = L

28/30L + 20 = L

Therefore 20 must equal 2/30L or 1/15L

L must be 15 x 20 = 300

Distance travelled = 300 -20 = 280

Let 'L' be total distance.

Day one distance covered = 1/3L

Day two distance covered = ¼ x 2/3L = 1/6L

Day three distance covered = 2/5 of remainder = 2/5 x L – (1/3L + 1/6L) day one and day two distances subtracted from total distance L

= 2/5 x L – (1/2L)

= 2/5 x 1/2L = 2/10L = 1/5L

Day four distance covered = 1/10L half of day three

1/3L + 1/6L + 1/5L + 1/10L +20 = L

10/30L + 5/30L + 10/30L + 3/30L + 20 = L

28/30L + 20 = L

Therefore 20 must equal 2/30L or 1/15L

L must be 15 x 20 = 300

Distance travelled = 300 -20 = 280

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 22:24

er No

Should I give you the answer then you can work backwards?

Should I give you the answer then you can work backwards?

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 22:43

I think my poor tired old brain has had enough tonight.

I'll maybe resume tomorrow.

I hope my methodology is sound, I suspect my maths is letting me down.

The only other way is to work back from day four, but that does't seem

right because the question is worded from the start of the journey.

I'll maybe resume tomorrow.

I hope my methodology is sound, I suspect my maths is letting me down.

The only other way is to work back from day four, but that does't seem

right because the question is worded from the start of the journey.

**myg**- Posts : 300

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## Re: Mensa Mind teaser

on Thu Jan 04 2018, 23:18

They have travelled 17/20ths of the distance .3/20ths = 20 miles left .The distance travelled so far is 17x 20/3= 113.3r miles

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 14:55

Oh happy days. Spot on MYG

**myg**- Posts : 300

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 16:10

Ray was doing well up to day 4,

1/3+1/6+1/5 means 14/20 travelled in first three days as he had worked out.

1/3+1/6+1/5 means 14/20 travelled in first three days as he had worked out.

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 16:17

I’m pleased with your explanation myg, and feel good that I got it partly right.

I did have another think about it this morning, but couldn’t come up with anything new.

Being an ex design engineer I think of myself as being a logical thinker, but most engineering problems are solvable with known tried and tested formulas.

Brain teasers like this one demand a more radical free thinking mind.

You seem to excel at these logic problems, I don’t know how you do it, well done.

I did have another think about it this morning, but couldn’t come up with anything new.

Being an ex design engineer I think of myself as being a logical thinker, but most engineering problems are solvable with known tried and tested formulas.

Brain teasers like this one demand a more radical free thinking mind.

You seem to excel at these logic problems, I don’t know how you do it, well done.

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 16:17

indeed he was MYG. My brain was getting addled at that time.

Anyway here is another to get your teeth into.

Two vehicles set off from the same point to travel the same journey.

The first vehicle has a start of six minutes before the second vehicle sets off.

If the first vehicle travels at 70 km/h and the second vehicle travels at 90 km/h, how many kilometres from the starting point will they draw level?

Anyway here is another to get your teeth into.

Two vehicles set off from the same point to travel the same journey.

The first vehicle has a start of six minutes before the second vehicle sets off.

If the first vehicle travels at 70 km/h and the second vehicle travels at 90 km/h, how many kilometres from the starting point will they draw level?

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 17:30

I've just had me 'tea', and I'm on it

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 17:46

Here is my solution.

I didn’t have any plan before setting off, just to write down my thoughts as I went along.

70 kph = 70/60 = 1.166kpm (kilometres per minute).

90kph = 90/60 = 1.5kpm

Difference in speed is 1.5 – 1.166 = 0.334kpm.

After 6 minutes the first vehicle will have travelled 1.166 x 6 = 6.996km.

The second vehicle will take 6.996/1.5 = 4.664 minutes to get to that point.

At the point where the second vehicle has reached the 6 minute distance, the first car.

will have travelled 6 + 4.666/1.166 = 9.147km.

At that point there will be 9.147 – 6,996 = 2.151 km distance between them.

Dividing 2.151km by 0.334 (difference in speed) = 6.44 minutes.

.

The second vehicle will have travelled for 6 + 6.44 =12.44 minutes.

At 1.5kpm that should be 12.44 x 1.5 = 18.66km.

They will draw level at 18.66km.

I didn’t have any plan before setting off, just to write down my thoughts as I went along.

70 kph = 70/60 = 1.166kpm (kilometres per minute).

90kph = 90/60 = 1.5kpm

Difference in speed is 1.5 – 1.166 = 0.334kpm.

After 6 minutes the first vehicle will have travelled 1.166 x 6 = 6.996km.

The second vehicle will take 6.996/1.5 = 4.664 minutes to get to that point.

At the point where the second vehicle has reached the 6 minute distance, the first car.

will have travelled 6 + 4.666/1.166 = 9.147km.

At that point there will be 9.147 – 6,996 = 2.151 km distance between them.

Dividing 2.151km by 0.334 (difference in speed) = 6.44 minutes.

.

The second vehicle will have travelled for 6 + 6.44 =12.44 minutes.

At 1.5kpm that should be 12.44 x 1.5 = 18.66km.

They will draw level at 18.66km.

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 17:54

Poor Ray. He does like to over complicate matters.

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 17:55

@Hieronymous wrote:Poor Ray. He does like to over complicate matters.

LOL , yes I do mon ami!!!!!!!!!!!!

Back to the drawing board.

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 20:58

Another bash, with a different tack:-

70 kph = 70/60 = 1.16kpm (kilometres per minute).

90kph = 90/60 = 1.5kpm

Distance equals speed x time

Let t = time Car 2 travels to draw level

Car 1 Car 2

6 x 1.16 + 1.16 x t = 1.5 x t

7 + 1.16t = 1.5t

7 = 1.5t – 1.16t

7 = 0.34t

t = 7/0.34 = 20.6

Distance = 20.6 x 1.5 = 30.9km

The cars meet at 30.9km

70 kph = 70/60 = 1.16kpm (kilometres per minute).

90kph = 90/60 = 1.5kpm

Distance equals speed x time

Let t = time Car 2 travels to draw level

Car 1 Car 2

6 x 1.16 + 1.16 x t = 1.5 x t

7 + 1.16t = 1.5t

7 = 1.5t – 1.16t

7 = 0.34t

t = 7/0.34 = 20.6

Distance = 20.6 x 1.5 = 30.9km

The cars meet at 30.9km

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 21:06

Down a bit

**raymyjamie**- Posts : 12707

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 21:17

I can't catch a break can I LOL

Is it a whole number?

I was a bit more confident with my maths and method on that one.

Is it a whole number?

I was a bit more confident with my maths and method on that one.

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 21:23

The expression 6 x 1.16 is 6.96, I rounded it up to 7.

If I use 6.96 the the final answer is 30.7km

If I use 6.96 the the final answer is 30.7km

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 21:24

I dont think so

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## Re: Mensa Mind teaser

on Fri Jan 05 2018, 21:28

Then again it might be

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