I thought a fairly straight forward teaser might ease us into the last weekend of the year.
And we can each check our solution using SteveD’s Pascal Triangle method [1; 4; 6; 4; 1] 
I think it would be good to tidy up a few loose ends before the year is out (in the UK).
Here is my solution to the second ‘Complete Focus’ teaser. It did need the involvement of the diagonals to keep the numbers down to 30 or less, whereas the first such teaser didn’t
Cheers
Don
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Starting at the top -
260
148; 112
82; 66; 46
36; 46; 20; 26
7; 29; 17; 3; 23
Cheers
Don
They both had ice-cream all over their face.
Well done Winky.
Wishing you and your family a Happy, Healthy and Prosperous New Year.
Cheers
Don
I think one is 448.
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I think you are correct Mike. Well done !
There are two or three other solutions … if anybody is keen
993
995
540
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Hi …yogi !
Nice set of numbers, however …
… the teaser asks for “… a three-digit number in which all the digits are even numbers”
You’re on the right tracks, so I bet (hope ?) you will find a couple of numbers that fit the bill. eg, you already know how to make a ‘zero’
I think 844 also works
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240
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I think so too. As with 240.
Nicely done.
I don’t have a definitive list, but I think there is still scope …
246
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Oops
Yep !
We’ve all been there, done that
But you gave it a good shot !
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The National Lottery
Ok, I kid myself that I am only making a 4-week contribution to charity and that the prospect of “winning” anything in the National Lottery is merely incidental. Otherwise, given the odds of winning any significant sum of money would finally confirm my place in that group that is referred to as the mathematically challenged.
However, this evening, Mrs D and myself were in our local corner shop buying 4 pints of milk in one of those plastic bottles when I realised, incorrectly, – by the way, none of what I have described so far is at all relevant to the up-coming teaser – that my current Lottery Ticket had expired last night (Wednesday). So, I asked Mrs D to wait a moment whilst I got the till assistant to check my Ticket for the past 4 weeks. “No winning numbers, sir” came the call from the assistant, “However, your ticket does have one more day to run, ie this Saturday.” Well, this was a welcome surprise, even though I had already filled out the necessary paper slip for the next 4 weeks.
I was about the proffer this slip to the assistant, when Mrs D said “No! Wait until Sunday, you don’t need TWO tickets for Saturday, you can only win once !.” I did as I was told (I’ve had 50 years of training !).
On the walk back home, I began to wonder … If my numbers came up on Saturday and there were, say, one hundred other winners of the Jackpot, then for sure, to all intent and purpose I WOULD double my share of the Jackpot if I had two tickets. On the other hand, if my numbers were unique to me, two tickets would still only deliver the whole Jackpot, certainly not two jackpots.
However, if just one other person held the same numbers as me, I certainly wouldn’t double my winnings by simply having TWO tickets. Or would I ?
You wouldn’t, but your winnings would increase by a third.
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Well done Mike.
10/10 plus another ‘one’ for taking the time and trouble to read through and decipher the long-winded text .
Brave man !
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Subtraction … and Square Eyes !
I have been helping my two young grandsons with their arithmetic these past few weeks.
They needed a bit of practise with subtraction. Rather fortunately I discovered a little fun-game for them to play that seems to have helped.
They select any four whole numbers from 1 to 12 inclusive and place them at the corners of a square.
They work out the difference between the numbers at each corner and write each difference at the mid-point of that side of the square. (There are no negative differences, only positive differences)
They join the mid-points to form a diamond, which now has already got a whole number at each corner and the process is repeated, forming alternate squares and diamonds until each of the mid-point values is Zero – which they will always be – eventually.
I have reproduced one of their examples below, which started with 1, 3, 9 and 12. You will notice that there are five squares in total (diamonds are simply squares rotated 45 degrees), including the final square with four zeros.
I also noticed, that on a few occasions they generated six or seven squares. So, I challenged them to pick the initial four whole numbers such as to maximise the number of squares required to reach four zeros.
They managed to generate nine squares, which I thought was very good and told them so.
However, I generated 10 and am reluctant to spoil their sense of achievement.
In fact you might find it easier to generate 10 squares rather than nine !
