"As a retired math teacher, I can tell you that by reversing the digits representing my current age and increasing the result by 13 you get my age reduced by 50%."
How old is she?
Just in case there was a trick regarding ages being represented in different bases, I checked all bases from 2 to 36 and ages from 1 to 120.
There was one solution in base 10 indicating that the teacher is 82 years old.
Reversed is 28, add 13 yields 41 which is half of 82.
Solutions in other bases:
The 4 columns are the base, the age represented in that base, the age in base 10, the result of the calculation (base10)
2 1001100 76 38
3 2220 78 39
5 240 70 35
7 130 70 35
10 82 82 41
15 20 30 15
18 62 110 55
28 10 28 14
31 31 94 47
If we stick to base 10 and allow the age to become ridiculously large, an interesting pattern emerges, age and age/2:
82 41
964 482
9784 4892
97984 48992
979984 489992
9799984 4899992
97999984 48999992
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Program One
for base in range(2, 37):
for age in range(1,121):
base_age = base2base(age, 10, base)
modified_age = int(base2base( str(base_age)[::-1] , base, 10)) + 13
base_modified_age = base2base(modified_age, 10, base)
if modified_age == age/2:
print(base, base_age, age, modified_age)
Program Two
for age in range(1,100000000):
modified_age = int( str(age)[::-1]) + 13
if modified_age == age/2:
print ( age, modified_age)
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Posted by Larry
on 2024-01-17 11:34:40 |
Solution
