快猫短视频

 

#181 A loss for words

set by Alison Kiddle

Wendy Wordsmith prides herself on her prowess at all the latest online word games. In fact, she hadn鈥檛 lost a single game since she started playing her latest obsession a couple of months ago. But after being caught out by an alternative spelling, she was dismayed this morning to see her winning streak drop from 100 per cent to precisely 98 per cent.

Since the app rounds percentages to the nearest whole number (9.5 per cent would round up to 10 per cent), how many more games does she need to win without another loss till her game tells her that she is back to 100 per cent?

Solution next week

#180 Neat as a PIN

Solution

The PIN is 10256.

Call the five-digit number 鈥淣鈥� and the additional added digit and multiple 鈥淢鈥�. Putting M at the beginning of N makes the number 100,000M + N, and putting M at the end makes it 10N + M.

So M 脳 (10N + M) = 100,000M + N.

Rearranged, this becomes N = M(100,000 鈥� M) 梅 (10M 鈥� 1).

If M = 1, then N = 11111, which can鈥檛 be the PIN as the digits are the same. The only other value of M that makes N a whole number is M = 4, with N=10256, and 102564 脳 4 = 410256.