Eight Edditions

Number Theory Level 2

A malfunctioned calculator has only two keys working '8' and '+'. A calculation of 24 can be done by using the keys "8+8+8". What is the least number of times that the '8' key can be used to calculate the sum of 1000?

Image Credit: Wikimedia Spring days


The answer is 8.

View wiki
Arpit MIshra by Arpit MIshra , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Arpit MIshra
Mar 31, 2015

888 + 88 + 8 + 8 + 8 = 1000 888 + 88 + 8 + 8 + 8 = 1000

Number of Times Eight pressed: 8 \boxed{8}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Brock Brown
Mar 31, 2015

This program tries every combination of buttons shorter than 888 + 88 + 8 + 8 + 8 888+88+8+8+8 until it finds it:

Python 2.7: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
 
from itertools import product
def goal(buttons):
    try:
        return eval(buttons) == 1000
    except Exception:
        return False
working = '8+'
pressed = 1
solved = False
while not solved:
    for guess in product(working,repeat=pressed):
        buttons = ''.join(guess)
        if goal(buttons):
            print buttons
            solved = True
            break
    pressed += 1
print "Answer:", buttons.count('8')

It then counts the number of eights in the calculation and finds 8 \boxed{8} of them.

I hope to see more malfunctioning calculator problems!

1 Helpful 0 Interesting 0 Brilliant 0 Confused

In this case, the quickest way to get near 1000 with 8 is typing 888+88 = 976. And 976+24 = 1000. So, to get 1000 , we must add 888+88+8+8+8.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You can't do it because the equals button doesn't work lol jk

Nate Clark - 5 years, 9 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...