Download Place Value, Integers, Ordering and Rounding

NRICH Short Problems
Place Value, Integers, Ordering and Rounding
Solutions for Mixed Selection 3
1. If there are two 5p pieces, this gives one way.
If there is one 5p piece, then there are two 2p coins, one 2p coin or no
2p coins, with all the other coins as 1p coins.
If there are no 5p coins, there are between 0 and 5 coins that are 2p,
and all the rest are 1p.
Therefore there are 1+3+6=10 ways to give change.
2.
Sunday
Monday
Tuesday
Day Max
4°
5°
−1°
Night Min
−1°
−5°
−3°
So on Wednesday morning the Maximum recorded temperature is
5° and the Minimum−5°.
3.
Consider numbers whose first digit is 1. Looking at each possible
value for the second digit we find 9 such numbers:
110, 121, 132, 143, 154, 165, 176, 187, 198.
Similarly there are 8 numbers starting with 2; 7 numbers starting
with 3... Lastly there is only one number starting with 9: 990.
Hence the total is 9+8+7+6+5+4+3+2+1 = 45.
These problems are taken from the UKMT Mathematical Challenges (ukmt.org.uk).
nrich.maths.org/9255
© University of Cambridge
NRICH Short Problems
Place Value, Integers, Ordering and Rounding
4.
From the second row we see that
c, d, e are 1, 2, 4 in some order;
and from the third column we see
that e> 2. Hence e=4 and we may
now deduce that g=8 and so f=5.
(Although their values are not
required, it is now also possible to
deduce that c=1, a=3, b=9, d=2.)
5.
As the sum of the integers is 1, it is clear that at least one of them is
negative.
Their product is positive so it may be deduced that exactly two of the
integers are negative.
Now we need to find three factors of 36 such that the largest is 1
greater than the sum of the other two. These are 6, 3 and 2.
So the answer is 6, -3 and -2.
If you want to see these problems individually on the site, they appear
under the following names:
1.
2.
3.
4.
5.
Loose Change (nrich.maths.org/6238)
Highs and Lows (nrich.maths.org/6262)
Central Sum (nrich.maths.org/2347)
Mini Kakuro (nrich.maths.org/5767)
Sum One Special (nrich.maths.org/5008)
These problems are taken from the UKMT Mathematical Challenges (ukmt.org.uk).
nrich.maths.org/9255
© University of Cambridge