Brain Teasers are Back!

Yep, column width limited. I could have increased the width and retained more sig figs.


I goofed when I drafted the second “Road from X to Y” teaser. I’ll correct it and re-post tomorrow.

The Road from X to Y. (2nd attempt !)

Our Local Council is building a new road from Village X to Village Y but hasn’t made much progress to date. In fact, they have only completed a few sections as shown on the plan below.

The numbers along the top of the plan and down the side of the plan show how many sections of road will be built in each column and each row. The planned road will not cross itself at any point.

Each cell on the Plan can only contain :-

a straight length of road either horizontally or vertically on the plan or

a turn to the right or a turn to the left (or up/down)

Can you complete the Plan ? (hopefully, this time you can !)

I’ll post my solution to the above X to Y road scheme tomorrow.

Meanwhile, a few simple bits of arithmetic to get the old grey cells working …

A) 3 children can eat 3 ice creams in 9 minutes. How long will it take 5 children to eat 5 ice creams ?

B) 4 lumberjacks chop down 12 trees in a day. How many trees could 13 lumberjacks chop down in a day ?

C) 5 mathematicians take 20 hours to solve a problem. How long would it take 25 mathematicians ?

Usual maths rules apply. ie the situations are hypothetical and “fair” eg with the mathematicians, you could argue that if the problem has already been solved by the first 5 mathematicians, any old maths teacher could subsequently solve it in a couple of minutes !!! :sunglasses: Let’s just stick with the hypothetical ratios.

A) 9 mins
B) 36 trees, or 39 depending on how they work.
C) 4 hours

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C) Mrs R says that it would take 5 minutes to leave a cryptic clue in the margin and 350 years to finally prove the theorem.


I have often wondered just what Fermat had by way of proof. And I bet that Andrew Wiles must have occasionally wondered if there was a simple, short-cut proof :sunglasses:

Well done Mike.

We’ll go with the 39 for part B.

The “teaser” was lifted directly from my grandson’s Key-Stage 3 Maths book ie 11-13 year olds. It also asked for a formula. The formula in the answers was T =3L where T = number of trees and L = number of lumberjacks.

I bundled the three “teasers” together, simply because I found myself having to think very carefully when checking his homework which included a random mix of Direct Proportions and Inverse Proportions.

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As noted yesterday, here is my solution.

Hope anyone who tried it, enjoyed it.

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Unless it takes 4 of them to fell each tree…

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Nice one Mike. I guess No. 13 could be the Foreman ? or these days the Health & Safety manager ?

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Some (simple) arithmetic

A) Use the numbers 2, 3, 4 and 5 (once each), plus the symbols + and = to make a valid equation. You can use the + symbol as often as you like.

B) Use that group of numbers again, plus any mathematical symbols you like, to make a different valid equation. Both sides must be equal. Not > or < than or any other non-equality. Just equal.

My very simple answers are:

a) 2 + 5 = 3 + 4

b) 3 - 2 = 5 - 4

Are we really looking at something as simple as these?

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For B) I had for example:

5 - 3 = 4/2


Hi Mulberry, the simple answer is “yes” - so well done. And for b) we could also have 5 - 3 = 4 - 2

I felt that a very simple, straightforward teaser was needed after posting the Deck of Cards Deal = 52!
I thought that anybody who had tried to get their head around the enormity of 52! deserved an easy break !

Hopefully back to “normal” again soon :sunglasses:

For b) my initial response was 5 + 4 = 3^2

Hi Mulberry, and others who try any of these teasers. I said above “back to normal again soon”. I’m not sure there actually are any “normal” teasers, but I hope anyone browsing this thread will find this next one interesting. I found I had to dust off the old memory sensors to satisfy myself that I knew the reason for the early part of the sequence !

Just continue the following sequence with the next two or three entries ……

1, 1, 2, 6, 24, …………

The second term is the first term multiplied by 1.
The third term is the second term multiplied by 2.
The multiplier keeps increasing by 1, so the sixth term is 24 x5, then 120 x 6, then 720 x 7 and so on.



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