Can sevens make 2023?
Add numbers written only with the digit 7. Reach 2023 using as few numbers as possible.
The clock starts when you reveal the puzzle.ONE DIGIT. A VERY DIFFERENT DESTINATION.
Only sevens.
As few as you can.
Add a little.
Notice the last digit.
YOUR DESTINATION
2023.
0
0
0
7777 already exceeds the target. These are the only numbers small enough to use.
YOUR SUM0
NUMBERS USED0
A blank page. A single digit.
Tap a tile to add it. Use − to remove one. Only addition is allowed.AT YOUR OWN PACE
A brain snack, with room to think.
THE ANSWER OPENS ANOTHER DOOR
Now for the lovely part.
You have an answer. Explore how it works, then take the idea somewhere new.
See why it works ↓Keep your time
THE IDEA BEHIND YOUR ANSWER
The final digit
sets the minimum.
Your sum is a construction. The ones column explains why no shorter sum could work.
YOUR SHORTEST SUM
…3
START AT THE RIGHT-HAND EDGE
Every term ends in 7.
If you add k all-seven numbers, their ones digits add to 7k. The sum must end in 3. For k from 1 to 10, the last digits are:
1 terms7
2 terms4
3 terms1
4 terms8
5 terms5
6 terms2
7 terms9
8 terms6
9 terms3
10 terms0
The first 3 appears at nine terms. More generally, 7k ends in 3 exactly when k ends in 9. So a positive number of terms must be at least nine.
Your nine-term sum reaches 2023. The lower bound and the construction agree: nine is the minimum.
The idea to take away
Look at the part of a number that every operation must respect. A single digit can rule out every shorter construction.