ONE EIGHTH CONTEST 2025
Prempeh College - 62 points
Suhum SHTS - 37 points
Benkum SHS - 13 points
ONE EIGHTH CONTEST 2025
Mfantsipim School - 53 points
Anglican SHS, Kumasi - 37 points
Sogakope SHS - 24 points
ONE EIGHTH CONTEST 2025
Adisadel College - 82 points
St. Hubert Seminary SHS - 24 points
Serwaa Nyarko Girls' SHS - 24 points
ROUND 1
PREAMBLE
Express the given number as a sum of two squares of Natural Numbers
FIRST QUESTION
193
ANSWER: $7^{2}+12^{2}$
SECOND QUESTION
145
ANSWER: $1^{2}+12^{2}$ or $8^{2}+9^{2}$
THIRD QUESTION
157
ANSWER: $6^{2}+11^{2}$
PRACTICE QUESTIONS
1. Express 65 as a sum of two squares of natural numbers.
ANSWER: $1^2+8^2$ or $4^2+7^2$
SOLUTION
Subtract each square from 65 and check whether the result is a square:
$65-1^2=64=8^2$
$65-2^2=61$
$65-3^2=56$
$65-4^2=49=7^2$
$65-5^2=40$
$65=1^2+8^2=1+64$
$65=4^2+7^2=16+49$
2. Express 85 as a sum of two squares of natural numbers.
ANSWER: $2^2+9^2$ or $6^2+7^2$
SOLUTION
Subtract each square from 85 and check whether the result is a square:
$85-1^2=84$
$85-2^2=81=9^2$
$85-3^2=76$
$85-4^2=69$
$85-5^2=60$
$85-6^2=49=7^2$
$85=2^2+9^2=4+81$
$85=6^2+7^2=36+49$
3. Express 89 as a sum of two squares of natural numbers.
ANSWER: $5^2+8^2$
SOLUTION
Subtract each square from 89 and check whether the result is a square:
$89-1^2=88$
$89-2^2=85$
$89-3^2=80$
$89-4^2=73$
$89-5^2=64=8^2$
$89-6^2=53$
$89=5^2+8^2=25+64$
4. Express 113 as a sum of two squares of natural numbers.
ANSWER: $7^2+8^2$
SOLUTION
Subtract each square from 113 and check whether the result is a square:
$113-1^2=112$
$113-2^2=109$
$113-3^2=104$
$113-4^2=97$
$113-5^2=88$
$113-6^2=77$
$113-7^2=64=8^2$
$113=7^2+8^2=49+64$
5. Express 41 as a sum of two squares of natural numbers.
ANSWER: $4^2+5^2$
SOLUTION
Subtract each square from 41 and check whether the result is a square:
$41-1^2=40$
$41-2^2=37$
$41-3^2=32$
$41-4^2=25=5^2$
$41=4^2+5^2=16+25$
6. Express 97 as a sum of two squares of natural numbers.
ANSWER: $4^2+9^2$
SOLUTION
Subtract each square from 97 and check whether the result is a square:
$97-1^2=96$
$97-2^2=93$
$97-3^2=88$
$97-4^2=81=9^2$
$97-5^2=72$
$97-6^2=61$
$97=4^2+9^2=16+81$