Detective Work on Calcrostic Problems
Solving a calcrostic is like
checking out a crime scene for clues. The following are examples, how to
get clues from single lines of the puzzle.
For example, if the row, column or diagonal is
- a × b = a
then a must be 0 or b must be 1. It is easy to find out which case applies. We look at other lines that include a and b. For example, if a=0 then c + a = c and if b=1 then c + b = d. Similarly, from a ÷ b = a follows a=0 or b=1 and from each of cd × b = cd, cd ÷ b = cd follows b=1. - a + b = cd
then it follows that c=1 because the sum of two 1-digit numbers can not be more than 9+9=18 and if both are different then not more than 9+8=17. The same conclusion can be made from cd − b = a.
- a × b = c
then what is special is that the result is only a one digit number, so less than 10. Also, a, b, c are all different, so none of them can be 1 or 0. Thus, one of a, b must be 2 and the other one 3 or 4 and c is 6 or 8. The same conclusion can be drawn from c ÷ b = a.
- a × a = b
then b is a square number unequal a and b<10, so a=2, b=4 or a=3, b=9. - c + ea = eg
then the first digit (the tens) in ea and in eg are the same, so we conclude that c + a = g. - c + ea = fg
then the first digit (the tens) in ea and in fg are different. This can only be due to a carry over, so we conclude that e + 1 = f and c + a = 10 + g.
- What can be concluded from
a × a = ba ?
Which values can a, b only have?
- What follows from
eb × c = cd ?
Which value can e only have?
- If you know that g = 1 then what does fg ÷ c = d tell you about f, c, d ?
Have fun!
Scheduled Contests
(on Wednesdays)
FEBRUARY 15TH, 2012APRIL 18TH, 2012
MAY 9TH, 2012
Previous Results
Caribou_Jan_18_2012_Grade_7_8
Top 10
1st
Milan Digiuseppe
Bishop E.Q. Jennings, ON
Bishop E.Q. Jennings, ON
2nd
Yixin Jiang
Dolphin Senior P.S., ON
Dolphin Senior P.S., ON
3rd
Jarod Morgenroth-rebin1
Allan Drive Middle School, ON
Allan Drive Middle School, ON
4th
Jeffrey Dawson
Citadel Middle School, BC
Citadel Middle School, BC
5th
Thomas Farrell
Citadel Middle School, BC
Citadel Middle School, BC
6th
Kevin Park
Bliss Carman Middle School, NB
Bliss Carman Middle School, NB
7th
Darren Cheung
Westmount P.S., ON
Westmount P.S., ON
8th
Jennifer Kim
North & South Esk Regional High School, NB
North & South Esk Regional High School, NB
9th
Alex Foley
Centennial P.S., ON
Centennial P.S., ON
10th
Alexandre Macdonald
École François-Buote, PE
École François-Buote, PE
Caribou_Jan_18_2012_Grade_5_6
Top 10
1st
Evan Feld
Dolphin Senior P.S., ON
Dolphin Senior P.S., ON
2nd
Shiv Kathuria
Sandhills P.S., ON
Sandhills P.S., ON
3rd
Willie Lei
Sandhills P.S., ON
Sandhills P.S., ON
4th
Soorna Choheili
Aurora Senior P.S., ON
Aurora Senior P.S., ON
5th
Lauren K
William Dunbar P.S., ON
William Dunbar P.S., ON
6th
Sean Wang
Irwin Park Elementary, BC
Irwin Park Elementary, BC
7th
Derek Xu
Erin Centre Middle School, ON
Erin Centre Middle School, ON
8th
Lyndon T
Laurelwood P.S., ON
Laurelwood P.S., ON
9th
Zaki Sayyid
Empire P.S., ON
Empire P.S., ON
10th
Frank Yi
Kwayhquitlum Middle School, BC
Kwayhquitlum Middle School, BC
Caribou_Jan_18_2012_Grade_3_4
Top 10
1st
Michael Yang
Adrienne Clarkson E.S., ON
Adrienne Clarkson E.S., ON
2nd
Navya Sheth
Oakville Public Library, ON
Oakville Public Library, ON
3rd
Kerwin Ho
Aurora Senior P.S., ON
Aurora Senior P.S., ON
4th
Zed L
Laurelwood P.S., ON
Laurelwood P.S., ON
5th
Ananya Chadha
Havergal College Junior School, ON
Havergal College Junior School, ON
6th
Michael Li
Doncrest P.S., ON
Doncrest P.S., ON
7th
Steven Zhang
Forest Hill Jr. & Sr. P.S., ON
Forest Hill Jr. & Sr. P.S., ON
8th
James Iansavitchous
Blessed Kateri, ON
Blessed Kateri, ON
9th
Nathan Cushing
Eagle Ridge Elementary, BC
Eagle Ridge Elementary, BC
10th
Sean Vasserman
Michael Cranny E.S., ON
Michael Cranny E.S., ON