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Numbers too big to compute, step by step

Multiply a hundred sevens together.

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The question

What day of the week will that be?

Only the leftover moves the day

from:Monday· days:135
MoTuWeThFrSaSu
19×7=133
135−133=2
Monday+2=Wednesday
  1. Two things are given and one of them is far too big to count through: today is Monday, and the wait is 135 days.
  2. Counting 135 days one at a time is not a method, so use the thing days of the week do: they come back round every 7. A whole week later is the same day you started on, and that is true of any number of whole weeks.
  3. So take the whole weeks out and they change nothing. 19 weeks is 19 × 7 = 133 days, and 135 − 133 = 2 days are left over. Only those 2 move the day at all.
  4. Now count 2 on from Monday — and count the day AFTER today as one, because today is where you are, not a day of waiting. That lands on Wednesday.

How it works.

  1. 01

    Two things are given and one of them is far too big to count through: today is Monday, and the wait is 135 days.

  2. 02

    Counting 135 days one at a time is not a method, so use the thing days of the week do: they come back round every 7. A whole week later is the same day you started on, and that is true of any number of whole weeks.

  3. 03

    So take the whole weeks out and they change nothing. 19 weeks is 19 × 7 = 133 days, and 135 − 133 = 2 days are left over. Only those 2 move the day at all.

  4. 04

    Now count 2 on from Monday — and count the day AFTER today as one, because today is where you are, not a day of waiting. That lands on Wednesday.

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