Puzzles
More doubling cribbage
Source: Inspired by Math Puzzle of the Week blog
Brendan and Adam are playing lots more games of high stakes cribbage: whoever
loses each game must double the other players money. For example, if Brendan has £3 and Adam has £4 then Brendan wins, they will have £6
and £1 respectively.
In each game, the player who has the least money wins.
Brendan and Adam notice that for some amounts of
starting money, the games end with one player having all the money; but for other amounts, the games continue forever.
For which
amounts of starting money will the games end with one player having all the money?
Doubling cribbage
Source: Math Puzzle of the Week blog
Brendan and Adam are playing high stakes cribbage: whoever loses each game must double the other players money. For example, if Brendan has £3 and Adam has £4 then Brendan wins, they will have £6 and £1 respectively.
Adam wins the first game then loses the second game. They then notice that they each have £180. How much did each player start with?
What is the sum?
What is \(\displaystyle\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{15}+\sqrt{16}}\)?
24 December
Today's number is the largest possible remainder which can be obtained when dividing one of
the answers in this advent calendar by another answer smaller than it (not
including today's answer!).
23 December
This number is a prime number. If you treble it and add 16, the result is also prime. Repeating this will give 11 prime numbers in total (including the number itself).
22 December
What is the largest number which cannot be written as the sum of distinct squares?
20 December
Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums reading across and down are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10.
| + | - | = 8 | |||
| - | - | - | |||
| + | ÷ | = 9 | |||
| + | ÷ | × | |||
| + | × | = 108 | |||
| = 6 | = 1 | = 18 |
The answer is the product of the digits in the red boxes.
19 December
1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/16. This is the sum of 5 unit fractions (the numerators are 1).
In how many different ways can 1 be written as the sum of 5 unit fractions? (the same fractions in a different order are considered the same sum.)