快猫短视频

#215 Trivia Tuesday

Set by Zoe Mensch

The team members were assembled for their regular meeting with their eccentric manager.

鈥淏efore we get to the main agenda, we鈥檒l observe our weekly 鈥楾rivia Tuesday鈥�. Today鈥檚 trivia titbit is that the month and day are the same number. It is 4 April, which is the fourth day of the fourth month. How about that?鈥�

The rest of the office rolled their eyes. 鈥淪eems like the boss forgot until the last second again,鈥� whispered Grace. 鈥淚 guess he just got lucky with the date.鈥�

Clancy thought for a moment. 鈥淪adly, it isn鈥檛 the only time this year when he鈥檒l be able to use the same kind of 鈥榯rivia鈥� for Trivia Tuesday.鈥�

Without looking at a calendar, can you work out how many more Trivia Tuesdays after 4 April will fall on the nth day of the nth month?

Solution next week

#214 Seven up!

Solution

The number is 7630.

Call it ABCD. BCD is divisible by 7, and since ABCD is also divisible by 7, A can only be 7. Similarly, since ABC is divisible by 7, there can be no remainder when D is divided by 7, so D can only be 7 or 0 鈥� and 7 is already ruled out as no digit is duplicated. The number BC must therefore also be a multiple of 7, i.e. 14, 21, 28, 35 etc. The sum of the digits in the number that is made by adding all digits of the code is only 7 if B and C are 6 and 3: In other words, 7+6+3+0=16, and the digits 1+6=7.