快猫短视频

#235 Sneak a peek

Set by Katie Steckles

At the funfair, 10 pots are stacked in a line along a shelf. Under two adjacent pots are the two keys that are needed to unlock the prize cabinet that contains a soft toy.

It costs 拢1 to enter the game, and all you have to do is guess which two pots you think the keys are under, for example you could say 鈥�8 and 9鈥� 鈥� but your odds of guessing correctly first time are low.

However, before playing you can also pay extra to 鈥渟neak a peek鈥� under one or more pots, at a price of 拢1 per pot. You can buy as many of these sneak peeks as you want, but you have to specify in advance how many you want to buy. You aren鈥檛 allowed to pay for extra ones after your first peek.

What is the least you need to spend on peeks if you want to guarantee that you will win the soft toy?

Solution next week

#234 Remember December

Solution

New Year鈥檚 Eve (and Craig and Maria鈥檚 first kiss) would have been on a Sunday. They gave gifts on every Monday and Thursday of December, and an equal number of gifts were given by both, so there would need to be the same number of Mondays as Thursdays. Given 31 days in December and seven days a week, there are always three consecutive days of the week that appear five times in the month, and four consecutive days of the week that appear four times. The only way for a Monday and Thursday to appear the same number of times is if they appear exactly four times each, with the first Monday falling on the 4th and the last Thursday on the 28th. So New Year鈥檚 Eve, 31 December, would have been a Sunday.