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Down for the count
Posted: Tue Apr 26, 2022 2:29 pm
by Gavin Chipper
This is another New Scientist puzzle, following on from
Squarebot. I don't think I need to explain why it might be relevant on a Countdown forum.
In the TV number quiz show Down for the Count, four contestants are challenged to combine each of five number cards exactly once to achieve a target number. They are allowed to use standard arithmetical operations +, –, × and ÷ (as well as brackets, if required).
“I’ll take five cards from the top row”, requested one of the contestants, and the presenter Anne-Marie obligingly revealed these five numbers:
10
100
1,000
10,000
100,000.
The studio computer then generated today’s challenge:
“Produce a whole number without any zeroes.”
No zeroes? Wow. Each of the four contestants thought hard, and after the timer ran out, each announced that they had used the five cards to produce a positive number smaller than 10. All four were different.
Which numbers did they get, and how?
I've managed to get 3 of the 4 so far and I'll post the details in a bit. See how you get on.
Re: Down for the count
Posted: Tue Apr 26, 2022 2:38 pm
by Thomas Cappleman
Got them all (last one took much longer than the first three)
Re: Down for the count
Posted: Tue Apr 26, 2022 4:26 pm
by Callum Todd
Same as T-Cap.
Re: Down for the count
Posted: Tue Apr 26, 2022 6:55 pm
by Adam Gillard
Got them all in about an even amount of time, maybe 90 seconds per answer. Good puzzle, thanks for sharing.
Re: Down for the count
Posted: Sat May 07, 2022 8:51 pm
by JackHurst
Nice puzzle
Re: Down for the count
Posted: Mon May 09, 2022 1:18 am
by Johnny Canuck
Happy to have cracked all four eggs in that Omelette!
Re: Down for the count
Posted: Mon May 09, 2022 9:34 am
by Gavin Chipper
I'm too thick to get the fourth one.
Re: Down for the count
Posted: Mon May 09, 2022 10:49 am
by Callum Todd
Gavin Chipper wrote: ↑Mon May 09, 2022 9:34 am
I'm too thick to get the fourth one.
The numbers you can make are:
1, 2, 5, and 9.
Now try.
Re: Down for the count
Posted: Mon May 09, 2022 1:37 pm
by Fred Mumford
I was in the "got three of them quickly, but took ages on the final one" club, but would be interested to know if we all struggled on the same number. The one that took me longest was the third in Callum's list, possibly because with the others I sort of knew those numbers must be gettable, whilst I wasn't overly confident on what the final one would be (although it did turn out to be the one I would have guessed as most likely).
Re: Down for the count
Posted: Thu May 12, 2022 2:03 am
by Dave Robjohns
Also in that club, but for me it was the first number. Was the most obvious one to start off searching for but eluded me until long after I'd found the others!
Re: Down for the count
Posted: Sat Nov 01, 2025 7:30 pm
by Gavin Chipper
Hi. I'm back. I just had another quickish look at this, and have seen how to get 3 of the numbers quite quickly. Pretty sure it was the same 3 as last time. I haven't looked at Callum's 4th number spoiler yet. I might get it down in text now though.
I think 1, 2 and 9 are all relatively easy, and it does kind of baffle me that there might be a different "4th number" for different people.
10 - (100,000/10,000)/(1000/100) = 9. I realise this might be a weird way of writing this, but I see it as 10 - 10/10.
((100000/10000)) + (1000/100) / 10 = 2. So (10+10)/10 = 2.
(100 - (100,000-10,000)/1000) / 10 = 1. So (100 - 90)/10 = 1.
Re: Down for the count
Posted: Sun Nov 02, 2025 7:48 pm
by Gavin Chipper
Right I think I have the last one:
1000/(100,000/10,000*10+100) = 5.
So you're getting 10 with 100,000 / 10,000 giving you 10, 10, 100, 1000. Then 10*10+100 = 200 and then finally 1000/200 = 5
I suppose this wasn't ridiculous, but still the hardest. I stumbled upon 1, 2 and 9 multiple times while trying to find the other one.
So I'm with Fred Mumford on which is the hardest one.
From the
New Scientist website (you might need to be logged in to see on the site):
#163 Down for the count
Solution
The contestants managed to get the answers 1, 2, 5 and 9. Here are possible routes to those numbers.
(((100,000 + 10,000) ÷ 1000) – 100) ÷ 10 = 1
((100,000 ÷ 10,000) + (1000 ÷ 100)) ÷ 10 = 2
10,000 ÷ (10 × ((100,000 ÷ 1000) + 100)) = 5
10 – (100,000 × 100) ÷ (10,000 × 1000) = 9