# Malware in the computer [closed]

You are IT staff working in a company and there are a few amount of computers which have some malwares in them.

• If you clean 3 computers every day starting today, you will be finished at the end of the day on Sunday.
• If you clean 5 computers every day starting today, you will be finished at the end of the day on Friday.

What day is it today?

## closed as off-topic by Peregrine Rook, Mithrandir, Alconja, Beastly Gerbil, IAmInPLSDec 25 '16 at 21:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Peregrine Rook, Mithrandir, Alconja, Beastly Gerbil, IAmInPLS
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Since we are finished at the end of the day,

it follows that the number of computers is divisible by 3 and 5. However, we do not know which multiple of 15 the number of computers is.

However,

if we let $a$ be the number of days cleaning 3 computers at a time, and $b$ be the number of days cleaning 5 computers at a time, we see $a\equiv b+2 \pmod 7$, due to the number of days between Friday and Sunday.

Also,

$5b\equiv 3a\equiv 3(b+2) \pmod 7$, so rearranging gives $2b \equiv 6 \pmod 7$, or $b \equiv 3 \pmod 7$. That means 3 days and some weeks will pass since starting to clean computers 5 at a time. Hence, 3 days and some weeks before the end of Friday would be the start of Wednesday.

In conclusion:

Without knowing the total number of computers, today is Wednesday.

• Yeah I got the same answer. – Beastly Gerbil Dec 24 '16 at 15:27
• @BeastlyGerbil Well, but your working assumes that the number of computers is the smallest possible. – Element118 Dec 24 '16 at 22:32
• anything bigger would result in you not finishing this week – Beastly Gerbil Dec 25 '16 at 9:59

Today is

Wednesday

We take the

Lowest Common Multiple (LCM) of 5 and 3 which is 15. We divide that by the computers we clean that day, and then take it away from that day.

So

15/3 = 5. Sunday - 5 days = Wednesday
15/5 = 3. Friday - 3 days = Wednesday

I have included Sunday/Friday in the sums above, as it says 'you will be finished at the end of the day' meaning you worked on that day too.

• @Oray am I correct? – Beastly Gerbil Dec 24 '16 at 13:51