Can you find a five digit number which has no zeros no digit is repeated, where:
The first digit is a prime number.
The second digit is the fifth digit minus the first digit.
The third digit is twice the first digit.
The fourth digit is the third digit plus three.
The fifth digit is the difference between the first digit and the fourth digit.
Don't forget that 1 isn't prime, so 13,254 isn't allowed.
Last weekend I travelled to my sister's house in Glasgow, around 250 miles away. I started on Saturday morning at 7am, traffic was heavy in places, and at times I was stationary. I arrived sometime after lunch.
On Sunday, it was time to make my way home, over exactly the same route. I left my sister's at exactly the same time, 7am, however, this time I came straight home without any travel delays, arriving home just before lunch.
How likely is it that I was at exactly the same point at exactly the same time on both days?
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Hint: It's more likely than you might first think.
It's certain that I was in exactly the same place at exactly the same time on both trips.
This is perhaps easiest to see by asking my twin brother to make the return journey from Glasgow at the same time as I leave home on my way to Glasgow, on Saturday at 7am.
At some point during Saturday we will meet, and therefore be at the same place at the same time. The fact I did the return journey the following day does not change this.
You have 12 coins, one of which is fake.
The fake coin is indistinguishable from the rest except that it is either heavier or lighter, but you don't know which.
Can you determine which is the fake coin and whether it is lighter or heavier using a balance scale and only 3 weighings?
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Hint: Finding the correct weighings requires some very careful thinking.
One solution is to label the coins with the letters FAKE MIND CLOT and weigh the coins in the following three combinations:
MA DO -- LIKE
ME TO -- FIND
FAKE -- COIN
Logic will now allow you to find the fake coin based on the three results. Bearing in mind we don't know whether the fake coin is lighter or heavier.
For instance, if the results were left down, balanced, left down, we could work out which coin is fake in the following way:
From the middle weighing we know that the coins METOFIND are all normal. So one of the coins ACKL is fake. Therefore looking at these coins one at a time in the other two weighings, we can see that:
A - appears on the left twice and could be fake.
C - appears only once, therefore can't be fake (otherwise the first weighing would be balanced).
K - appears on opposite sides, so it can't make the left side go down both times.
L - appears only once, therefore can't be fake (otherwise the third weighing would be balanced).
Therefore the only possibility is A, which must be heavier. Any other combination of ups and downs will allow you to use the same logic to find the fake coin.
Daft Dave did such a good job of the housing estate, he was asked to paint the room numbers on all of the doors of the fourth floor of the local hotel.