快猫短视频

#126 More chocs-a-weigh

Quality Control at the WonderSnack chocolate factory used to have a problem with one of the six machines that produce 200 gram chocolate bars (see puzzle #109 Chocs-a-weigh, 17 April, p 52).

That faulty machine has been scrapped, but Hazel Nutt, the new quality control manager, has discovered that the same issue has cropped up in at least one of the remaining five machines. Faulty machines are producing bars that are each 5 g below the required 200 g weight.

鈥淗mm,鈥� thinks Hazel. 鈥淟ast time, we worked out which machine was at fault with a single weighing of a selection of bars taken from each machine. I think I can do the same this time. But I鈥檒l need a machine that can weigh up to, oh, about 6.5 kilograms.鈥�

Why 6.5 kg? And how many bars from each of the five machines must she add to the scales for this weighing?

#125 Digital printing

Solution

Kevin has enough of every digit except the twos 鈥� he is one short. The book needs 38 ones, which means it has 112 pages.

In the first 99 pages, every digit except zero appears 20 times, 10 of them in the units place (1, 11, 21, 31, etc.) and 10 in the tens place (10, 11, 12, etc.).

From 100 to 112, a one is used another 18 times (13 as a hundreds digit, and three in the tens and two in the units), making 38 ones altogether.

By the time we get to page 112, we have seen 21 of every digit except for the two, which is needed 22 times.