An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Choose any three by three square of dates on a calendar page...
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
The ten numbers in the star total 75.
Each number appears in two "lines".
And there are five lines, making a total of 150. Which implies the total for each line is 30.
This means that R+I=24 and therefore R=11 and I = 13 (or vice versa).
If R=11 then N=12, H =10 and C=11 which is impossible.
If R=13 then N = 10; H = 12 and C= 9, which is correct.
once you know that each line adds up to 30 we can set up the following equations:
$(1) 4+N+R+3=30 ⇒N+R=23$
$(2) 1+R+I+5=30 ⇒R+I=24$
$(3) 3+I+C+7=30 ⇒I+C=20$
$(4) 4+H+C+5=30 ⇒H+C=21$
$(5) 1+N+H+7=30 ⇒N+H=22$
Then we are going to use a trick to “isolate R” by alternately adding and subtracting equations to get what we want, so consider
This problem is taken from the UKMT Mathematical Challenges.