Trial and error using even numbers for the pennies and 1 thru 9 at the front.
Fortunately I started at the low end so didn’t have to do more than a dozen trials.
Nice teaser btw.
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I then wrote a short Excel spreadsheet just to be sure there was only one solution. It was just a bit quicker than manually checking the rest of the possible solutions.
Trial and error is often a good technique, with a bit of intuition to narrow down to a manageable set of possible solutions, so well done!
My alternative went as follows:
The total is a multiple of 72 = 8 x 9 which means it must be a multiple of 8 and 9.
As 1000 (£10.00) is divisible by 8, we only need to consider the last 3 digits. 792 is divisible by 8 and is the only possibility starting 79.
All numbers divisible by 9 have a sum of digits that is divisible by 9. As 3+6+7+9+2 = 27, this means the first digit must be 3.
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I am stood on the bank of a river that is 100m wide. I know that I can swim steadily at 10 kph and the river is flowing at 8 kph. (kph = kilometres per hour).
What is the shortest length of time it will take me to swim across the river ?
Fools rush in–I think it’s the same as if there were no current, 0.01 hour, since the current is at a right angle to his desired direction of travel.
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I sense a red herring. Swimming at 10 km/h for a distance of 100 m would take 100/10000 = .01 hours, or 36 seconds. The speed of the current just means you don’t reach the other bank opposite your starting point, you are further downstream.
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Don has been hiding his light under a bushel all these years. If he can swim at 10kph (and that’s “steadily” apparently!), he is quite a bit faster than the current world record holder for 100m who can only manage 8kph! 
Anyway, by my reckoning, for every 10m he swims across, he is moved 8m to one side. Using pythag, that means he will swim 12.806m on the hypotenuse, so for a 100m wide river he will need to swim 128.06m which will take around 46 seconds.
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JR and Mike - well done.
Steve, his speed over the river bed will be quite high, i get 12.806 kph, but his progress across the river will remain based on his 10 kph swimming. or alternatively covering a distance of 12.806 m at the enhanced speed of 12.806 kph.
Note: I cheated when I said I could swim at 10 kph - this was an hypothetical superman !
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I am stood on the bank of a river that is 100m wide. I know that I can swim steadily at 10 kph and the river is flowing at 8 kph. (kph = kilometres per hour).
How long will it take me to swim across the river to the point opposite me on the other bank ? In other words, I don’t want to drift downstream with the river flow so I am going to have to lay off quite a bit of drift !
Don, I get your drift so I will answer this teaser in a minute.
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Nice reply Ravvie, i’ll give it a few more minutes to allow others to respond before we reveal the answer.
Just a hunch, but did I inadvertently give the right answer to the second part with my incorrect answer to the original question?
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Steve, you had the right idea but teasers involving Pythagoras nearly always lead to nice round numbers.
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60 Seconds.
Although, the speed of flow of a 100m wide river will no be constant across it’s width.
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Not quite Steve.
Assume the river is flowing left to right. The second question requires the swimmer to head something like 50 deg to the left of the opposite bank. This counteracts the drift due to the river flow.
The vector diagram comprises a right angle triangle with a hypotenuse of 10 kph (swimmer), the longer side of 8 kph (river speed) and a shorter side of 6 kph (track made good and speed of the swimmer over the river bed).
I think your solution showed the track made good and speed over the river bed when the swimmer headed directly across the river and drifted down stream with the current.
Got try to keep these teasers conceptually plain. But you are absolutely right about river flows.
Obviously a good answer as well Frank.
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Magic Dates
My birthday falls on a magic date, in that DDxMM=YY. It is 18 April ‘72.
Mrs R is just under three years younger than me. Her birthday is 25 March ‘75, also a magic date.
Considering the 20th century, what is the closest age gap for a couple where both have different magic date birthdays?
(Mrs R wants it known that the dates are fictional and are just for the purposes of this teaser!)
So, in principle, we are looking for a pair of dates something like 03/02/06 and 02/03/06, but closer together than 27 days ?
That’s it exactly. 27 days is a pretty good start, though it can be bettered.
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